How you gonna pack bits onto a physical chip except to put them into a cube? What’s the longest path in a cube? What’s the average path length in a cube? They’re all functions of the surface area of the cube.
Yes, but that's not at all how we're packing bits into physical chips right now. The fact that access latency is O(N^[1/3]) has nothing to do with this, it's just that the relative size of caches and memories have been designed that way.
That this latency is of the same order as if you were putting bits in a cube is more coincidental than anything.
A bound can exist due to multiple factors. If you fixed the other bound, speed of light would still dictate a growth rate higher that the volume of a cube.
That is artistic license, and you know it. Do you have access to a tesseract? If so why the hell are you on HN?
Edit to add: And on further reflection, this won’t save you. Because the heat production in the hypercube is a function of internal volume, but the heat dissipation is a function of the interface with 3D space, so each hypercube is limited in size, and must then be separated in time or space to allow that heat to be transferred away, which takes up more than O(n^(1/3)) distance and distance means speed of light delays.
There is no beating the speed of light. You cannot stack servers like cordwood. So no matter what toroidal internetworking architecture you make the maximum interconnect length is always, always a function of the dimensions of the devices and typically with a constant factor of. 5x to 10x on top.
Star interconnects are limited to the surface area of each device, which is the cube root of the volume. Because you have to have space to plug the wires in.
“You’ve got it all figured out” is deflecting basic physics facts. What is your clever solution to data center physics?
