So one visualisation of a sphere in very high dimensions is not something smooth and round, but something that is somehow simultaneously very symmetrical, and y

So one visualisation of a sphere in very high dimensions is not something smooth and round, but something that is somehow simultaneously very symmetrical, and yet also very spikey. It's unlikely that this will help anyone, but I recently learned that the spiky protrusions a naval mine are called "Hertz horns": http://www.popsci.com/blog-network/shipshape/terrible-thing-waits-under-ocean http://www.popsci.com/blog-network/shipshape/terrible-thing-... So if for some reason you are trying to trying to make a loose analogy to the spikiness of hyperspheres to an older military mariner who has never seen a hedgehog, you could clarify by saying "you know, like the Hertz horns on a sea mine?"