The Fourth Dimension

by Charles Howard Hinton

But how, when every act of thought is of things in space, and time, and ordered, shall we represent to ourselves that perfectly indefinite somewhat which is Kant’s necessary hypothesis—that which is not in space or time and is not ordered. That is our problem, to represent that which Kant assumes not subject to any of our forms of thought, and then show some function which working on that makes it into a “nature” subject to law and order, in space and time. Such a function Kant calls the “Unity of Apperception”; i.e., that which makes our state of consciousness capable of being woven into a system with a self, an outer world, memory, law, cause, and order.

The difficulty that meets us in discussing Kant’s hypothesis is that everything we think of is in space and time—how then shall we represent in space an existence not in space, and in time an existence not in time? This difficulty is still more evident when we come to construct a poiograph, for a poiograph is essentially a space structure. But because more evident the difficulty is nearer a solution. If we always think in space, i.e. using space concepts, the first condition requisite for adapting them to the representation of non-spatial existence, is to be aware of the limitation of our thought, and so be able to take the proper steps to overcome it. The problem before us, then, is to represent in space an existence not in space.

The solution is an easy one. It is provided by the conception of alternativity.

To get our ideas clear let us go right back behind the distinctions of an inner and an outer world. Both of these, Kant says, are products. Let us take merely states of consciousness, and not ask the question whether they are produced or superinduced—to ask such a question is to have got too far on, to have assumed something of which we have not traced the origin. Of these states let us simply say that they occur. Let us now use the word a “posit” for a phase of consciousness reduced to its last possible stage of evanescence; let a posit be that phase of consciousness of which all that can be said is that it occurs.

Let a, b, c, be three such posits. We cannot represent them in space without placing them in a certain order, as a, b, c. But Kant distinguishes between the forms of sensibility and the concepts of reason. A dream in which everything happens at haphazard would be an experience subject to the form of sensibility and only partially subject to the concepts of reason. It is partially subject to the concepts of reason because, although there is no order of sequence, still at any given time there is order. Perception of a thing as in space is a form of sensibility, the perception of an order is a concept of reason.

We must, therefore, in order to get at that process which Kant supposes to be constitutive of an ordered experience imagine the posits as in space without order.

As we know them they must be in some order, abc, bca, cab, acb, cba, bac, one or another.

To represent them as having no order conceive all these different orders as equally existing. Introduce the conception of alternativity—let us suppose that the order abc, and bac, for example, exist equally, so that we cannot say about a that it comes before or after b. This would correspond to a sudden and arbitrary change of a into b and b into a, so that, to use Kant’s words, it would be possible to call one thing by one name at one time and at another time by another name.

In an experience of this kind we have a kind of chaos, in which no order exists; it is a manifold not subject to the concepts of reason.

Now is there any process by which order can be introduced into such a manifold—is there any function of consciousness in virtue of which an ordered experience could arise?