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Your Mind Is Eight-Dimensional – How Algebraic Topology Is Unlocking [video] (youtube.com)
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"


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 :-D

FYI, 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:


Thinking about thinking in certain ways for certain people could be an existential risk (akin to a recursive stack overflow or to a self-modifying program overwriting its own essential code?) -- just like the story of the centipede tripping over itself and being unable to walk when it thinks about where to place its feet instead of just walking.

That said, people who tend to be extremely focused like these two people (Chris McKinstry and Push Singh, dead at 38 and 33 respectively) mentioned in the Wired article you linked to may also sometimes neglect other aspects of their life that support good health (sunlight & vitamin D, good nutrition with a variety of phytonutrients and omega-3s from whole foods instead of eating quick-to-ingest junk foods, regular exercise, family, friends, community, sleep, spirituality, time in nature, and so on). They may also be exposed to environmental toxins related to their work.They might also be inclined to take risks most other people would not. Or they may some unresolved underlying personal issues that lead to their focus in the first place. Or they may have seemingly-random accidents as with Singh having chronic back pain from an injury -- although perhaps if he had been stronger from these other factors he would not have been so badly injured from moving furniture or might have recovered quicker? Depression is also a condition that leads to rumination -- so there may be some overlap among those who ruminate a lot from a tendency to depression (even as part of bipolar transitions for McKinstry) and those who do deep dives into how the mind works.

There are a lot of tragedies in this world -- but there are also a lot more AI researchers, philosophers, mathematicians, and librarians than the two mentioned in the Wired article who are living healthier lives. For example Marvin Minsky and Isaac Asimov both lived to old age (88 and 72 respectively). Immanuel Kant and Jean-Paul Sartre made it to 79 and 76 respectively. My undergraduate advisor at Princeton, George A. Miller, who started WordNet just as I was graduating, lived to 92. Marvin Minsky had been one of George's first advisees -- I was one of George's last ones.

On the original article link to the video of the design of the mind and "eight dimensions" -- while no one knows for sure, it seems the brain is a combination of different systems that are adapted for different purposes and represent external state, internal state, and goals in different ways. Conscious beings like humans can switch which of these subsystems they are most attending to at any one time (or perhaps consciousness may reflect a switch arising from non-conscious processes). Marvin Minsky talked about this as a way of problem solving -- representing problems topologically, linguistically, and in other ways and then picking the representation that seems most productive at any given time to move closer to goals. So maybe there is something equivalent to an eight dimensional representation in the brain, but I would tend to doubt it is the only way the brain represents data.

Alternatively, if one interprets the video as just being about one suggested way of modelling the brain with an eight dimensional representation and simplices and simplicial complexes -- sure, with Turing equivalence, there are lots of systems that can model anything. The question is more (similar to the previous point on the brain itself involving multiple representations), in what contexts is the model useful and how does it compare in that way with alternative representational systems? It may be a great choice in most cases, but that can't be determined from the video alone. However, we can also run the same software on a lot of different hardware, and lots of different software on the same hardware, so a good analysis of human neural hardware as typically eight dimensional may still not tell us that much about the software that actually runs on it or that could or should run on it.

Also, models tend to simplify things in order to be cost-effective to use for some purpose. Another HN article from today is about "Brain Cells Share Information with Virus-Like Capsules" which may be related to long-term memory perhaps being encoded in RNA. So, where does that indirect communication fit in an eight-dimensional model based on direct neural connections andhow neurons directly cause each the to activate? https://news.ycombinator.com/item?id=16139798

Broadly spreading hormones in the brain also may add another indirect communication layer of complexity not represented in this eight-dimensional model.

To circle back to the Wired article, McKinstry and Singh seemed focused on some sort of linguistic encoding of knowledge with their Mindpixel and Open Mind projects. While linguistic knowledgebases may potentially be useful, as above, language is only one way the brain represents information. And as useful as language is for communicating or storing certain types of knowledge, language may not even be the primary way most humans think most of the time -- especially given humans are such visual creatures, and as above, all the larger variety of information processing systems in the brain which are constantly running alongside human language processing.

Speculatively, one can wonder if a certain apparent narrowness in both McKinstry's and Singh's thinking about intelligence might have connected to not thinking more broadly about their own lives and what could have been possible? And sadly, often additional schooling as in Singh's situation just makes people even narrower: http://disciplinedminds.tripod.com/ Although one might think that was less true around the MIT Media Lab and in Marvin Minsky's orbit? Also, the lack of a basic income might create a lot of unneeded financial stress like in McKinstry's situation where he pursued a commercial approach via a questionable "stock" offering that may have alienated him from a larger open source and academic community or produced worries about returns to investors? Of course, a lot of happy people have PhDs and/or work at companies that sell stock -- so those choices and their consequences are not a whole explanation either. As with the brain itself, cause and effect in a complex network of interactions can be essentially impossible to explain in a simple way.

It's also sad that two people with some similar ideas and ambitions seemed to be in more conflict than harmony, which probably was not helpful to either of their mental states. Related: http://www.alfiekohn.org/contest/ "Contrary to the myths with which we have been raised, [Alfie] Kohn shows that competition is not an inevitable part of “human nature.” It does not motivate us to do our best (in fact, the reason our workplaces and schools are in trouble is that they value competitiveness instead of excellence.) Rather than building character, competition sabotages self-esteem and ruins relationships. It even warps recreation by turning the playing field into a battlefield. No Contest makes a powerful case that “healthy competition” is a contradiction in terms. Because any win/lose arrangement is undesirable, we will have to restructure our institutions for the benefit of ourselves, our children, and our society."

Fascinating story, terrifying situation... and much nostalgia for how great WIRED was before they made it into just yet another general-interest lad's magazine.

Any finite graph can be embedded in three-dimensional space without edge crossing. [1]

Thankfully the human connectome doesn't need eight-dimensional space to exist.

[1] https://link.springer.com/article/10.1007/BF02522826

Yeah, but, like 3-D spaces are like so last year. ;)

Also, paywall free version of paper: http://brainmaps.org/pdf/graph.pdf

I had to recommend to most people I shared this with to check out the previous video first: https://www.youtube.com/watch?v=rlI1KOo1gp4

"Your brain can be modeled as a simplicial complex, and Algebraic Topology can tell us the Betti number of that simplicial complex..." is not the most layman-friendly way to introduce a video... :)

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