Dimensions — First Draft

Dimensions:

I am trying to set forth a new hypothesis through this document.

I want to clarify certain points before I start this exercise:

  • This is not a mathematical hypothesis. As such there is no mathematical treatment. Wherever I have used numbers, I have used them for the sake of convenience and ease of demonstration rather than as equations.
  • This does not take into account already existing scientific/mathematical treatments of this topic (e.g. Penrose’s singularity theorem, Hurst exponent, Poset Dimension etc )
  • This is not a philosophical treatment of this topic either. It does not attempt to massage any of the existing philosophical work on this subject.
  • Any co-incidence with similar existing thought processes is purely incidental and not a work of conscious plagiarism.

Existing ground:

Dimension (as defined in Wikipedia):

In common usage, a dimension (Latin, “measured out”) is a parameter or measurement required to define the characteristics of an object—i.e. length, width, and height or size and shape. In mathematics, dimensions are the parameters required to describe the position and relevant characteristics of any object within a conceptual space —where the dimensions of a space are the total number of different parameters used for all possible objects considered in the model.

The key words that I want to delve into in this document are:

“parameter or measurement required to define the characteristic of an object”

The key “parameters” that we have chosen as dimensions today are space and time. Words like length, size, shape etc are space-specific; words like past, present, future etc are time-specific. There is yet another set of words like velocity, pace, acceleration etc that are derivative in nature i.e. they are derived by forming calculations on the space and time dimensions of an object.

Definitions and Assumptions:

These are the definitions that I will employ during my hypothesis. If the reader’s definitions of these terms are at variance with those mentioned below, this hypothesis will not be able to answer the challenges coming from such quarters

Object: A physical entity, something that is tangible and within the grasp of the senses.

Characteristic: A distinguishing/unique feature of a person or a thing.

Hypothesis statement:

Each object has an infinite number of dimensions and even a minute change in any of these dimensions will result in the creation of an entirely different object.

Suppose there is an object A with the following co-ordinates (a1, a2, a3……an). Suppose we change one of the dimensions from a1 to b1. Then the object at the co-ordinates (b1, a2, a3….an) will be an object B which is different and unique from object A.

Let us define what the dimensions are that form these co-ordinates a1, a2 and so on and forth.

Let there be an object A. Let there be a point O with co-ordinates (0, 0, 0…..0). Let us assume for the sake of convenience that the number of dimensions is finite and equal to a number ‘n’.

Let point O be the “zero point” or “start point” for our hypothesis.

Let there be a point O1 which is at a distance of 1 meter from point O. (for the sake of simplicity, we will assume that this distance is towards the north in the horizontal space). Following our conventions, the co-ordinates for this point are (1, 0, 0….0)

Now let there be point O2 which is at a distance of 1m and a height of 1m from O.

Following our conventions, the co-ordinates for this point are (1, 1, 0….0)

Now let there be point O3 which is at a distance of 1m, a height of 1m and a time of 1 hour from O.

Following our conventions, the co-ordinates for this point are (1, 1, 1….0)

Now let there be point O4 which is at a distance of 1m, a height of 1m, a time of 1 hour and a temperature of 1degree centigrade from O.

Following our conventions, the co-ordinates for this point are (1, 1, 1, 1 ….0)

Taking this forward by a few points we can come up with similar “parameters” or “characteristics” of objects like pressure, weight, colour, stability and so on and so forth.

We will assume (again, purely for the sake of convenience) that we have finite number of such “parameters” or “characteristics” or “dimensions”. We will assume that there is a point ‘On’ which is at a single unit of all dimensions from O such that its co-ordinates are (1, 1, 1 … 1)

Now consider object A which is initially at point O.

Let us change the dimensions of this object A such that it is now at point ‘On’.

This hypothesis states that the object at point ‘On’ is not A, but B – B being unique and different from A.

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