The Rev Dodgson said:
roughbarked said:
The Rev Dodgson said:
OK, it is quite QI, but I wish they’d tried a bit harder at explaining what this 11 dimensionality actually means, rather than focusing on the gee-wizzness of it all.
Perhaps they don’t actually know yet?
I presume the mathematicians who define the maths know what it means.
I can hazard a guess. Nothing too special.
Think of a ball in 2-d (circle), it can be adjacent to up to 6 neighbours.
In 3-d (sphere) it can be up to 12 neighbours (face centred cubic).
In 4-d it can be up to 48 neighbours.
So presumably they’ve found a few cells each with very many synapses, and interpret synapses as “neighbours”. A typical neuron has “thousands of synapses”. So feed the number of synapses back into the number of nearest neighbours of an n-sphere to get a dimensionality n.
Even so, 11-d seems excessive.
Or perhaps …
Perhaps they’ve looked at individual cells and the ratio of surface area to volume. In higher dimensions the ratio of surface area to volume increases. That would be a less useful method.