Space must not be confused with the world, or universe, in so far as space has only three dimensions. On the other hand, the number of dimensions attributed to the world is always more than three. A four-dimensional world, with time being the fourth dimension, has been around for so long that it has become a virtual truism. An original thinker of modernity must choose a different number, rather than three or four--- either less than three or more than four. For understandable reasons, they all opt for a bigger number, although one or two might have treated us to a delightfully peculiar intellectual challenge.
This embryonic entry looks at the question of dimensionality as a philosophical problem. The key questions in this approach are: how many dimensions does the world have?, and how many countable dimensions would constitute the optimum amount, for our scientific and philosophical investigations?
We know that mathematically the number of dimensions is limitless, but what does it tell us, besides the fact itself? There is a demonstrable practical value in talking about the “normal” three spatial dimensions, plus we can throw time into the bargain, forming… four?
Not according to the Russian philosopher Peter Demyanovich Ouspensky, who has come up with the idea of a six-dimensional world. In his mind, the universe in time is also defined by three directional vectors. Like a non-dimensional point moving in one direction to create the one-dimensional line, its non-spatial movement in time only creates a one-dimensional entity, where time is the only dimension. But having formed a line in space, this one-dimensional entity can create a two-dimensional entity simply by traveling in time. Likewise a geometrical plane, traveling in time, creates a new dimensionality, and so does a traveling infinite cube... Ouspensky’s logic here allows him to double the three-dimensional world (rather than just to add a fourth dimension) to a total of six dimensions, but the reader could just as well pursue this kind of logic and come up, with the help of the dimensionless point, to the grand total of seven, not just six dimensions. But enough of this particular pursuit!
The reader may reasonably inquire about the practical use of coming up with a multidimensional world, like this one, and, except for the distinct pleasure of abstract contemplation, it is rather difficult to come up with a good rationale. Personally, I would like to limit the number of dimensions in this case to four: three space dimensions plus time, because four is a good starting point for further explorations. It makes it easier to add new dimensions to the sum total, such as, say, the dimension of thought. And indeed, different players of the dimensionality game have come up with quite a few other dimensional entities, bringing the total number to ten, eleven, twenty-six, and so on.
There is definitely great merit in the mathematical pursuit of infinite numbers of dimensions, and a tangible practical value in pursuing this matter in physics, relative to quantum field and string theories, and quantum mechanics. The single-word term spacetime is already commonly established, to convey “any mathematical model that combines space and time into a single continuum.”
But the question of dimensionality in philosophy has not been exhausted yet, by any stretch of imagination. It is possible for the free mind to venture into areas where the concept of dimensionality applies, which have been untouched yet, some quite surprisingly. For instance, I have a purely philosophical question, which, to my knowledge, has not been answered yet. How does the undiscovered realm of afterlife stand in relation to the abstract and concrete dimensions identified or envisaged so far? How many dimensions, and which ones, does the Kingdom of Heaven possess, and all the entities depicted in the Bible?
Mind you, it is not my intention to insult the non-believers in afterlife by my insertion of this much-disputed concept into an arguably scientific context of unquestioned reality. But we are talking about philosophy now and the concept of afterlife is a bona fide “unquestioned reality” in the kingdom of pure thought. Moreover, anyone familiar with advanced mathematics would know that it deals with concepts far more bizarre and out of this worldly than the relatively tame concept of afterlife, yet nobody disputes a direct, albeit surely arcane, connection between such extreme mathematics and the blurry outposts of the otherwise solid science.
Thus, to sum it all up, I am sure that unless and until the philosophico-mathematical discussion of dimensionality extends to the supernatural, or the “world beyond,” to be precise, our philosophical endeavors in this field will have fallen short of the mark; and, considering how far we have gone otherwise in our general abstract thinking, it is safe to say that in this area of human thought in particular, our efforts are sorely wanting.
This embryonic entry looks at the question of dimensionality as a philosophical problem. The key questions in this approach are: how many dimensions does the world have?, and how many countable dimensions would constitute the optimum amount, for our scientific and philosophical investigations?
We know that mathematically the number of dimensions is limitless, but what does it tell us, besides the fact itself? There is a demonstrable practical value in talking about the “normal” three spatial dimensions, plus we can throw time into the bargain, forming… four?
Not according to the Russian philosopher Peter Demyanovich Ouspensky, who has come up with the idea of a six-dimensional world. In his mind, the universe in time is also defined by three directional vectors. Like a non-dimensional point moving in one direction to create the one-dimensional line, its non-spatial movement in time only creates a one-dimensional entity, where time is the only dimension. But having formed a line in space, this one-dimensional entity can create a two-dimensional entity simply by traveling in time. Likewise a geometrical plane, traveling in time, creates a new dimensionality, and so does a traveling infinite cube... Ouspensky’s logic here allows him to double the three-dimensional world (rather than just to add a fourth dimension) to a total of six dimensions, but the reader could just as well pursue this kind of logic and come up, with the help of the dimensionless point, to the grand total of seven, not just six dimensions. But enough of this particular pursuit!
The reader may reasonably inquire about the practical use of coming up with a multidimensional world, like this one, and, except for the distinct pleasure of abstract contemplation, it is rather difficult to come up with a good rationale. Personally, I would like to limit the number of dimensions in this case to four: three space dimensions plus time, because four is a good starting point for further explorations. It makes it easier to add new dimensions to the sum total, such as, say, the dimension of thought. And indeed, different players of the dimensionality game have come up with quite a few other dimensional entities, bringing the total number to ten, eleven, twenty-six, and so on.
There is definitely great merit in the mathematical pursuit of infinite numbers of dimensions, and a tangible practical value in pursuing this matter in physics, relative to quantum field and string theories, and quantum mechanics. The single-word term spacetime is already commonly established, to convey “any mathematical model that combines space and time into a single continuum.”
But the question of dimensionality in philosophy has not been exhausted yet, by any stretch of imagination. It is possible for the free mind to venture into areas where the concept of dimensionality applies, which have been untouched yet, some quite surprisingly. For instance, I have a purely philosophical question, which, to my knowledge, has not been answered yet. How does the undiscovered realm of afterlife stand in relation to the abstract and concrete dimensions identified or envisaged so far? How many dimensions, and which ones, does the Kingdom of Heaven possess, and all the entities depicted in the Bible?
Mind you, it is not my intention to insult the non-believers in afterlife by my insertion of this much-disputed concept into an arguably scientific context of unquestioned reality. But we are talking about philosophy now and the concept of afterlife is a bona fide “unquestioned reality” in the kingdom of pure thought. Moreover, anyone familiar with advanced mathematics would know that it deals with concepts far more bizarre and out of this worldly than the relatively tame concept of afterlife, yet nobody disputes a direct, albeit surely arcane, connection between such extreme mathematics and the blurry outposts of the otherwise solid science.
Thus, to sum it all up, I am sure that unless and until the philosophico-mathematical discussion of dimensionality extends to the supernatural, or the “world beyond,” to be precise, our philosophical endeavors in this field will have fallen short of the mark; and, considering how far we have gone otherwise in our general abstract thinking, it is safe to say that in this area of human thought in particular, our efforts are sorely wanting.
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