Posts Tagged ‘Flatland’

Where and when we are – a dimensional conundrum

September 7, 2021

“In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it”. – Wikipedia

In the concept of spacetime one might think that (x,y,z,t) are the four dimensional coordinates which are necessary and sufficient to specify the location of any object at any time within our universe. But that would be an oversimplification. It is true only for a relative location and not for any absolute location.

In reality we have no idea – in absolute terms – of where we are or when we are.

The place where I was born on the surface of the Earth has – during my lifetime – drifted along with the continents some 2.3 m North-East across the earth’s surface. The Sun (along with the Earth) has moved 6.9 billion km around the centre of the Milky Way Galaxy. Using referents outside the Milky Way Galaxy, it has, during the same time, moved some 55 billion km in space. So, I was born some 60 billion km away from wherever in space we actually are now. In the context of the Universe this is still local space, and I do not need to account for the very expansion of space. The looming collision of the Andromeda Galaxy speeding towards us is still 4.5 billion years away and irrelevant in the scale of my lifetime. Taking my present location as (0,0,0,0) and the X-axis as the straight line from where we were then to now, the coordinates of my birth location become (-60, 0, 0, -73 years) where x, y and z are measured in billions of km.

Everything is relative to here and now.

It is not even certain that time is actually a dimension of the same kind as the 3 physical dimensions we perceive. Some think it emerges together with the Universe and everything. Others think it is just a facet of existence. In any event, we only experience it as a backdrop for, but separate to, our own individual existences. On the stage of our existences, we strut and fret our hours away, but we cannot interact with or impact the relentlessly moving backdrop. Just as with nonsense rhymes using language, nonsense equations by learned physicists about the theoretical access to past times is just nonsense. As with any language, mathematics can also describe the unreal and the nonsensical. Speculative cosmologists have more in common with Edward Lear than they would like to think.

Considering time to be a dimension is no more than a convention or, at best, an analogy. It does not help either, that

  1. we have no clear definition (or understanding) of what a dimension is, and
  2. we can take a dimension to be anything that can be counted.

We can measure the oscillation of apparent motions and assume that such motion is regular and then infer the passage of time. But what time is other than a magical, necessary backdrop for everything is beyond our comprehension. We cannot be certain that a second now is the same, or longer, or shorter, than a second at some other time. (A second now must be longer than a second was then).

The world is what our perception tells us it is. But our perception is limited, and it limits the boundaries of our reality. We perceive space and everything around us as having 3 dimensions, yet we cannot truly conceive of any real thing having other than three spatial dimensions. In our 3-dimensional world we can define one- and two-dimensional things only as concepts (lines and surfaces) but we cannot identify any real-world objects which have only one or two dimensions. Moreover, real things having more than 3 dimensions are beyond our comprehension. How a fourth spatial dimension could be manifested lies outside of human reason. We have the language to describe – but only conceptually – any number of dimensions. Scientists and mathematicians speculate about 3 or 7 or 9 or infinite dimensions and claim either that 3 is the most probable or theorise that the others are hidden in the strings that make up the world, but the human brain can only perceive 3. (I note in passing that invoking the infinite is itself an admission of incomprehensibility). It is a fruitless and inevitably circular discussion to question whether it is our perception which is limited to 3 dimensions or whether the universe has only three to be perceived. Our universe is enabled, and strictly constrained, by what our cognition allows us to perceive. Every real thing in our universe has three spatial dimensions; no less, no more. Our universe has 3 spatial dimensions because that is all, and only what, we can perceive.

I probably read “Flatland” as a teenager where a sphere in Flatland can only be perceived as a circle.

Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by “A Square”, the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella’s more enduring contribution is its examination of dimensions. – Wikipedia

No matter how many dimensions the universe may have, three dimensions is all human cognition can ever perceive. It is that reality which constrains all our thought. It becomes a fundamental assumption for science which the scientific method cannot penetrate. If other dimensions exist, then what we perceive in three are projections. As a shadow is perceived to be two-dimensional. But to have a projection or a shadow in our 3-dimensional world we would need some kind of cognitive light from the other, higher dimensions to create what we perceive.

But human cognition is limited. We cannot perceive what we cannot perceive. And we have no clue – earthly or divine – as to where and when we are.



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