Your Mind Is Eight-Dimensional – How Algebraic Topology Is Unlocking [video] 141 points by espeed on Jan 13, 2018 | hide | past | web | favorite | 19 comments

 (This is one of the few YouTube channels I subscribe to, pity this presenter left to concentrate on her doctoral thesis.)I suppose the “eight-dimensional“ reference in the title comes from there being “up to” eight-dimensional directed simplexes detected in the reconstructed neural networks?
 Here's the referenced journal article..."Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function"https://www.frontiersin.org/articles/10.3389/fncom.2017.0004...NB: The supplementary material PDF has graphs showing dimensions 0 through 7 (note the zero-based indexing so that's 8 total dimensions). https://www.frontiersin.org/article/10.3389/fncom.2017.00048...
 Yes, but the reference to eight-dimensionality is quite baffling. The peak of the population is at two, and there's a tail end far above.
 My guess is that: after eight dimensions in a [cross]linked neural network, it becomes very difficult to draw conclusive distinction between the operation of synapse in the observed brain and simulated synapse. I shall have to catch up on the domain reading before providing you with a thorough answer on "how did we arrive at 8?"Edit: Go to 6:01 in the video. There's a graph.
 There's nothing in any of the graphs that screams “eight dimensions” to me. Am I missing something?
 The number of dimensions is written across the bottom of the graph and 8 is right around the middle. It may be hard to see because of the video player bars.
 ~>> E8 ?
 Yes. Dimensionality can be a little tricky here; what's meant is that eight dimensions are required to express some of the simplices, if we were to interpret them geometrically.Honestly, I'm more interested in the cohomological features of this network, which would help us find loops and other curiosities in high dimensions. I figure that there have to be some interesting loops in there somewhere.
 As an applied mathematician (and one that put himself through the paces of the mental contortions necessary to understand Penrose's twistor theory) I reckon I'm one of the few people here that actually know what “cohomological” means, and agree with you.
 I agree that looking for loops would be interesting but they actually discard subgraphs without a source and a sink, i.e. loops.
 "Your mind is eight-dimensional" is pure clickbait, chosen by an editor to drive traffic. The claim has no substantive bearing on this presentation nor its underlying research whatsoever. Don't go crazy trying to figure out its secret meaning.The research itself is incredibly interesting— a good springboard question for the HN crowd would be to ask what ANNs have complex enough signal directionality that we could fruitfully run this form of geometric analysis on them?
 >Don't go crazy trying to figure out its secret meaning.There's no "secret meaning", and it doesn't refer to spatial dimensions. It has a very clear and very precise mathematical meaning.
 My first thought in seeing this : Terry Pratchett was right all along. We’re all wizards, and this is the manifestation human neural morphology to the octarine discharge of strong magical fields :-DFYI, I just finished “The Colour of Magic”, the first Discworld novel by Terry Pratchett, a few days ago and I’m currently reading its sequel.
 The guy who proposed this committed suicide because no one believe him: