this post was submitted on 09 Jan 2024
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This shape clearly can be oriented. There is a neck and a mouth. Get out of here with your dimension reducing depictions
It cannot in fact be oriented, regardless of the embedding and the dimension of the ambient space.
b-but it has no volume!
No, it has all the volume.
Only for 4D shapes, for 3D shapes they get suck in the little alcove in the middle, they can't percieve or travel along the 4th dimension so that little part is almost like a space "inside". Of course there isn't a space inside in actuality, the 3D space just gives that illusion, but for objects bound to the 3D world it is essentially the inside for all intents and purposes.