Teach Thy Necessity to Reason Thus,
The study of a compound of two square pyramids, and the drama of Idyllic nonsense.
November 24th, 2022
565 Alnitak Rd.
Imagine, please, two pyramids with a square base each. Now, move one of the pyramids on top of the other and rotate it so that each of the square faces are facing away from each other and the ‘points’ of the pyramids are touching– perfectly aligned. How would the resulting object look if the top pyramid would descend, phasing perfectly with the other pyramid, so that each base was at the same height as the other’s point, or tip?
I’ve been asking myself that question for the last couple of days. I can visualize it very clearly in my mind. However, when I attempted to sketch it out, some part or other of the figure seemed to be off– as if it were impossible to draw this bizarre conjunction!
Frustrated with my attempts to transcribe what I could imagine so effortlessly into a paper, I began my meticulous observation and ‘unfolding’ of the shape. Finally, I realized that, seen from the perspective from which I was drawing this curious shape, the foreshadowing effect of the pyramids made it so it seemed that one of the pyramids only had four faces, not five, and that it was not a square pyramid, but a triangular pyramid, otherwise known as a tetrahedron. In other words, my drawings were fine.
Thankfully, my efforts yielded results. However, what would have been of my visual idea of the conjunct pyramids if I never were able to illustrate it? I am sure I am not the first person to imagine this shape, but, for the sake of conversation, let’s assume I was. How would I’ve been able to share it with someone else?
I think I’m hinting at a well-known problem within the philosophy of language – that which suggests that what we cannot communicate cannot be said to be philosophically meaningful.
I keep failing to communicate and make appealing that mush of polyhedrons that knock around my hollow temples. I’m glad I had better luck with this actual polyhedron, though! It does pose the worrisome question, however, that there are so mental shapes which no drawing will be able to depict and some thoughts– or entire personalities– that for which language will simply not be a sufficient tool to communicate.
Hans Reichenbach, a philosopher and physicist, wrote in his Scientific Philosophy about this idea that there are “equivalent descriptions” of empirical phenomena. The idea is that there are, for example, two views of geometry, the Euclidean and the non-Euclidean. I am not a mathematician, but I believe the difference is that the Euclidean interpretation of geometry accurately describes the reality only at a local, or ‘human scale’, level. That is to say that, if we examine really large-scale objects, then a non-Euclidean interpretation of geometry is needed to accurately represent reality.
Goodman’s riddle of induction comes to mind as well. While we might talk about objects having the properties of ‘blue’ and ‘green’ according to the different colors that we perceive from them, imagine a different culture that refers to objects with a different, but ‘equivalent’, set of terms, such as ‘grue’ or ‘bleen’. Though both sets of terms relate to color, the rules, Goodman tells us, of ‘grue’ or ‘bleen’, are very weird (relative to us) and involve taking into account odd factors such as the time of the observation of the color of the object. Though all of these terms are ‘equivalent’, they are not identical. An object might be, by virtue of its color, both ‘green’ and ‘grue’. However, that does not imply ‘green’ and ‘grue’ mean the same thing.
Maybe I should take up painting instead of talking.