Thinking 4-D Introduction

continued

Let us put ourselves in this situation. We are faced with the '4th' dimension in the same way the Flatlanders are faced with our own - now we are the ones unaware of some strange space "hovering around us": before us lies a concept for which there is no sensory evidence - or for that matter, a space that would be "too complex" to understand even if we could detect it. There being no proof for its existence, the 4th dimension is perhaps no more real than the science fiction stories it is found in. What, then, is the solution to this problem?

The situation, as it has been stated so far, puts us in a sort of "sandwich": on one side, we have a dimension of space that we 'look down upon' (the 2nd dimension). On the other side, we have a dimension of space that we are 'looked down upon' by (the 4th dimension). This arrangement, at first, may seem frustrating - but it is a position, rather, that we should consider ourselves lucky to be in - a 'gold mine' of opportunity: it would appear that if the same concepts concerning the 3rd dimension that are hidden totally from a Flatlander (and as clear as day to us), happen to be the same concepts concerning the 4th dimension that are 'hidden totally' from us, then we can, via a certain system of reasoning, take advantage of this situation. Upon what, one may ask, is this reasoning based? It is a very simple, very powerful system of thought: that "analogues never lie".

And what is an 'analogue'? A product of the process known as analogy - the "tool" with which we will be working, and means by which we can "fill in the blanks" in places where there would 'otherwise be no answers'. First of all, by studying just what is 'detectable' and just what is 'hidden' from a Flatlander, we can get a good idea of where and in what ways the 4th dimension is 'hidden' from us. And once we have a better idea of just what it is concerning the 4th dimension that we are looking for, we can then refer back to the particular area of the 2nd dimension, that corresponds to what we are trying to understand about the 4th dimension - an area where which a Flatlander could be possibly pondering the same question about the 3rd dimension that we are about the 4th. We could perhaps even imagine what he is thinking - the specific questions, doubts, and frrustrations he has concerning that 'area' of study. But what is 'shrouded in mystery' to him, is as clear as day to us - and because it is, we can grasp the opportunity to bring the concept "up a notch".

To perform a 4-dimensional analogy, so to speak, we first examine the way in which a given 3-dimensional structure / process (of which a Flatlander would know nothing) exists 'in relation to' the 2nd dimension. Possessing this knowledge, we try to use it to 'simulate' a 4-dimensional version of the structure / process. And just how would this be done? By imagining how the '4-dimensional version' would affect / relate to / appear to the 3rd dimension: the way in which the 4-dimensional version 'interacts' with the 3rd dimension, take note, will always be very similar to the way in which the 3-dimensional version 'interacts' with the 2nd dimension. All analogues - the products of analogy - by their very own nature, will always possess properties and behaviors distinctly similar to the model from which they were constructed.

Interestingly enough, there's no reason why a Flatlander, in fact, could not undergo this process as well, to gain knowledge of our own dimension! How so? By means of the "Linelanders" - little sentient beings whose world happens to be 1-dimensional: an extremely limited world consisting only of length. Existence as a "Linelander" could probably be best described as being one of several "beads" distributed along an extended string: you would only be able to 'slide back and forth', and there's no way to get around your "neighbor" (like cars confined to a single lane). Nonetheless, as a tool for analogy, "Lineland" could prove invaluable.

There is, however, a side to constructing higher-dimensional analogues that can render the entire process unsuccessful: the "believability" of the analogues themselves. This is due to what could be called a sort of spatial "common sense" - a 'belief system' that originates from all sensory experience obtained from an existence limited to one's own dimension. That is, a 'rigidity of thought' as to what is and isn't spatially possible. As the means of being introduced to this concept we are to picture a line intersecting a 1-dimensional plane (another line) at a right angle. To those of us able to comprehend how a line can intersect a 1-dimensional plane at a right angle, we know as a fact that the line intersects the 1-dimensional plane at a point. Let us now assume that a Linelander occupies the 1-dimensional plane. What would the Linelander think of the point at which his 1-dimensional plane is intersected? To help the Linelander out, we tell him that the point he sees on his 1-dimensional plane is in fact a cross-section of a line (which it is). To those of us who externally view the Linelander's 1-dimensional plane and can perceive extension out from the 1-dimensional plane (and into the space above and below it), it is very agreeable that the point at which the line intersects the 1-dimensional plane is a cross-section of a line.

The Linelander confined to the 1-dimensional plane, however, would have a problem with this. The idea of the point at which his 1-dimensional plane is intersected being a cross-section of a line can be labeled only as invalid / absurd because in the mind of the Linelander, there is no 'above and below' the 1-dimensional plane he occupies: therefore because in the mind of the Linelander no directions exist into which both ends of the perpendicular line can extend, the Linelander's best possible conclusion is that the entire line exists within the point he sees on his 1-dimensional plane. It is not at all difficult to understand the nature of the Linelander's situation. Given the Linelander's predicament, what can we learn from this situation? What we see here is the 1-dimensional "common sense" of the Linelander taking action. This is a very healthy, very normal reaction to a higher-dimensional occurrence. What must be explained to the Linelander, quite simply, is that he is not to be alarmed about the doubt he is experiencing. We are to tell him that given the proper means of visualization, he can in fact envision the line perpendicular to the 1-dimensional plane he occupies. We have yet to encounter in the material to come what this 'means of visualization' would be, and how we could apply it to our own dimension. What else can we learn from the Linelander's situation? We can be made aware of an obstacle that not only the Linelander but we ourselves must overcome: the obstacle of letting one's spatial "common sense" control one's approach to higher dimensions.

By understanding how and why beings in the lower spaces show skepticism toward analogues that exist above their own dimension, we will be able to deal with skepticism that we may happen to face: and it is not a matter of if we face it - but simply when. And it is hence through analogy that we can 'transcend' the senses. The goal before us must be made clear - in that it is in finding these analogies that the real task lies!