How do we know that only one geometry is relevant to the complex happenings of nature? Perhaps a three-dimensional geometry is relevant to one sort of occurrences; and a fifteen-dimensional geometry is required for another sort.
Of course our more obvious sense perceptions seem to clamour for three dimensions, especially sight.
On the other hand, sound, though voluminous, is very vague as to the dimensions of its volumes, as between three or fifteen, for instance. Also, any change in scale, to the very small or to the very large, makes surprising changes in the characters of the happenings disclosed so far as we can observe. We have developed very special types of sensory observation; and in consequence we are wedded to a correspondingly special set of results, true enough if we introduce the proper limitations. But as our science expands, the area of relationship to other aspects of nature becomes increasingly important.
Perhaps our knowledge is distorted unless we can comprehend its essential connection with happenings which involve spatial relationships of fifteen dimensions.
The dogmatic assumption of the trinity of nature as its sole important dimensional aspect has been useful in the past. It is becoming dangerous in the present. In the future it may be a fatal barrier to the advance of knowledge.
Also, this planet, or this nebula in which our sun is placed, may be gradually advancing towards a change in the general character of its spatial relations.
Perhaps in the dim future mankind, if it then exists, will look back to the queer, contracted three-dimensional universe from which the nobler, wider existence has emerged."
— Alfred North Whitehead, Modes of Thought