
u/JustaguynamedTheo

How would a 4 dimensional Gabriel’s horn work? Would it have an infinite 3 dimensional volume but a finite 4 dimensional volume? Is such an object possible in other ways?
Gabriel’s horn or Torricelli’s trumpet is a paradoxical geometric figure with an infinite 2 dimensional volume, but a finite 3 dimensional volume. Would this also work in the 4th or even higher dimensions? There are also other shapes and figures theoretically possible with a finite volume but a infinite surface in 3 or even 2 dimensions. So would those ideas also work in the higher dimensions?
I saw a “How many diapers could he possibly use?” meme, where Patrick says “Japan was going to surrender before the nukes.” To which Spongebob lists the following:
-They refused to acknowledge the Potsdam Declaration
-They tried to negotiate to retain their conquests in China and South-East Asia
-They didn’t surrender after the first bomb
-They didn’t even immediately surrender after Nagasaki and the Soviet invasion of Manchuria
-Even after that they still tried to get the Allies to explicitly guarantee the survival of the Imperial System of Government
-Even after Hirohito agreed to surrender, the Army tried to launch a coup against him, even though he was legally considered a living god.
After these claims true or do they leave crucial information out?