The Human Brain Can Create Structures in Up to 11 Dimensions
sciencealert.com
sciencealert.com
“They found that groups of neurons connect into 'cliques', and that the number of neurons in a clique would lead to its size as a high-dimensional geometric object (a mathematical dimensional concept, not a space-time one).”
Edit-more to the point;
“"Networks are often analysed in terms of groups of nodes that are all-to-all connected, known as cliques. The number of neurons in a clique determines its size, or more formally, its dimension," the researchers explained in the 2017 paper.”
Also interesting that 11 is also a prime number. But equally, may just be one of life's coincidences and the human drive to see patterns and understand exactly what is going on - a trait that still advances humanity today.
I don't see gradient descent or back propagation in biology.
As for back propagation, I'm sure there are aspects in nature in which translate - maybe the nerves system of some species.
Way to see it is that evolutionary change of any form could in theory be modeled in machine learning. There may be aspects of evolution and how it operates that help refine how we do machine learning.
But regarding evolution implementing back-propagation, I agree that is just bonkers, as it would require cells to back-propagate in time information about death or procreation! If our biology implements information time machines, biology would be a lot weirder than it is (and it would imply that we could use that by sequencing an organisms genome (or ensemble of them) to read from the future, and keeping it fed without allowing reproduction, and later when we want to write information back either kill or let it reproduce).
That's just plain nonsense. There can't be back-propagation in evolution without biological time-travel of information.
And machine learning without back-propagation is basically a genetic algorithm, so the claim that "evolution has done a lot of work that we equate as machine learning" would then reduce to a widely accepted fact that nobody disputes and is thus uninformative: "evolution has done a lot of work that we equate as genetic algorithms"
To equate this into evolution, if you viewed a species as the model, each generation adapts to the previous generations experience, hence it feeds back into the next generation. That evolution may prevail or that whole lineage dies off. It gets down to the perspective of how you measure that time aspect and define the start point of your time perspective. In a simulation you are arbitrary resetting that time baseline on each model, so the equivalent would be to view the human as a baseline of each birth. yes it gets confusing, but to dismiss it just because you have no actual time-travel from a cosmological perspective and compare to an arbitrary time perspective that runs in a linear temporal realm of the universe is unfair.
But many things are hard to equate, you could say it is like comparing apples to pears, but then there are many perspectives in which you can compare them and find them equal. But you can't take one single perspective and transpose that upon another perspective and presume a conclusion.
if natural selection were to use back-propagation, then killing or allowing procreation would be measurable not only in the genome right after birth of an IVF organism, but even be measurable in the half genomes of the sperm and egg cells before they met (assuming we reach some non-destructe genome sequencing technology). That would simply make actual natural selection useless. Moreover, if all cells had this capacity, and our neurons are cells too, why don't I have this skill inately?
I stand by my opinion that natural selection does not employ timetravel, and hence also does not employ backpropagation
EDIT: adding, one does not need timetravel for backpropagation in the brain or in a computer, just enough memory or delay bandwidth to store the intermediate values for backpropagation. i.e. the feedback is nearly instantaneous, or low bandwidth from example to scoring, but scoring in natural selection depends on how much offspring one makes before one dies, how can this inform the choice mutations??
This particular claim has been making the rounds for quite some time. It's total rubbish.
I think you misread that. It means that the title is technically correct but relies on a different definition of the term 'dimension', not that the title is wrong.
What about, "The amazing connectivity of the human brain", or "Researchers unravel the mathematics of connections in the human brain"?
There's absolutely no need to confuse readers by conflating unrelated concepts.
I could make up my own definition of dimension, e.g. the dimension of a manifold needed to embed some bizarre variety with some cleverly defined homological correspondence to slices of brain material I looked at under the microscope, thought of as simplices. I might then get 276 dimensions. Do I then get a press release for this? It's utterly meaningless. "Mathematician discovers that our brains live in a 276 dimensional universe".
Except it clearly does, using the definition of the mathematics used to analyse connections.
> I could make up my own definition of dimension, e.g. the dimension of a manifold needed to embed some bizarre variety with some cleverly defined homological correspondence to slices of brain material I looked at under the microscope, thought of as simplices. I might then get 276 dimensions. Do I then get a press release for this? It's utterly meaningless
Just because we can make up words, all words that have different meanings in different contexts, are meaningless? I agree that perhaps not enough context was provided, but to say that the words itself do not have a certain meaning because you misunderstood the context in which it's used is ludicrous.
The world does not revolve around you.
>The world does not revolve around you.
The GP was quite careful to speak from the standpoint of a reader from a general audience. A work of writing does in fact revolve around its audience.
So was I, otherwise I wouldn't have said:
> I agree that perhaps not enough context was provided, but to say that the words itself do not have a certain meaning because you misunderstood the context in which it's used is ludicrous.
Regardless,
> The definition of a word derives from the mutually understood definition of the word between the author and the reader.
Of course, and the word is defined in the article. So if the reader had actually read the article given, rather than just commenting on the title, then they wouldn't have been confused.
So are we trying to raise or lower the quality of public discourse? If a journalist uses a technical term in a headline, and then goes on to explain what the term means in the article, how is that not fine? It sounds like you only want journalists talking at a eighth grade level.
Why don't you try to re-write the findings yourself then? I think you'll find it difficult to say the least. Your first obstacle might be finding a better word to describe the mathematical shape of the structures other than 'dimension'. That's what mathematicians use, why can't journalists use it too?
“We're used to thinking of the world from a 3-D perspective,”
Here 3-D clearly refers to our three spatial dimensions, and the article clearly abuses this definition of the term to contrast with the totally different meaning of “dimension” that is to come.
It’s fine to use non-intuitive mathematical definitions in a work for a non-expert audience, but you must clearly define them from the start — and not lead the audience astray by deliberately referencing the most common definition to form a contrast at the start of your piece.
The title was likely picked to be confusing on purpose as click-bait. Misleading headlines lower the quality of public discourse.
Misleading headlines only affect people who have not read the article. People who have not read the article, or can't bother to read the article, are essentially incapable of giving a proper high-quality response to the article.
I don't see how you can lower the quality of discourse any further than someone commenting on an article that they didn't read.
The article itself also continues to conflate the definitions of dimension by referring to 3-D. When little timmy draws a star on his paper we don't say "congrats on your 5 dimensional drawing".
Right, so don't waste other people's time by commenting on an article that you haven't properly read.
I don't wee where the term is ever very clearly explained, the best I see is:
>> the number of neurons in a clique would lead to its size as a high-dimensional geometric object (a mathematical dimensional concept, not a space-time one)
It is a "network topology" concept, the distinction between "mathematical" and "space-time" is nonsensical.
> That's what mathematicians use, why can't journalists use it too?
Not only is the term poorly explained, but it also appears to be used incorrectly. I don't think it is correct to talk about these structures being created in 11 dimensions, but that as "with 11 dimensions", "having a dimension of 11" or "being 11-dimensional" (which is how the term is used in the paper).
> It sounds like you only want journalists talking at a eighth grade level.
The problem is that the article is talking at about a 8th grade level using collegiate terms that it doesn't take the time to explain at at an 8th grade level. This doesn't help to elevate public discourse, it just sows misunderstanding.
> Why don't you try to re-write the findings yourself then? I think you'll find it difficult to say the least.
This seems needlessly combative.
In terms of accurate and responsible reporting of this science, I think the article that the author cites and paraphrases heavily is much more well written: https://www.eurekalert.org/pub_releases/2017-06/f-bbt060617....
If a marketing team uses a financial term in a commercial with an asterisk, and then goes on to explain what the term with an asterisk means in the actual 117 pages long financial contract this commercial is trying to sell, how is that not fine?
I think you probably object because "11 dimensions" sounds a lot like the 11 temporal dimensions of in certain space-time related theories. But this is a completely unrelated set of dimensions.
The article describes what are most definitely dimensions, but ... of the array sort, and not of the String Theory sort.
If I'm generous I could maybe believe that larger cliques form more complex connection patterns and can perform higher dimensional processing. But even this fails as the paper then goes on to describe the cliques and cavities as being higher-dimensional.
All that aside, I do think there's something to the paper, just using some poor choice of terms. It seems what's being described as complex is both the physical non-uniform pattern of connection and the subgraphs of activation which may be able to consider a high number of dimensions for a given input stimulus. I couldn't follow the Simplices/Complexes/Betti numbers to see how it relates to a measure of dimension.
To add a little clarity to what the hallucinations look like, checkout what people describe here: https://psychonautwiki.org/wiki/Geometry
The process of hallucinating on LSD feels like you're sliding a window through a higher dimensional structure projected onto a 2D plane. LSD hallucinations aren't "3D" in the same way that mushroom hallucinations are. LSD feels like infinite 2D planes stacked on top of each other, rather than a 3D, if that makes any sense.
If you pause to meditate and quiet your mind, you can get the hallucinations to briefly stall or at least retain their current character. If you focus on one area and let your mind explore the hallucinating you're looking at and just sort of "let it happen", or perhaps change music/environments/stimulus, you can push the hallucinations in a new direction.
The 2D nature of the hallucinations and the lens-like focusing mechanic does give the impression that you're viewing a projection of a higher dimensional space.
I understand it sounds like woo, but the experience is remarkably similar to the feeling of playing with something like http://4dtoys.com/ and I can very much understand what mirimir is describing.
I don't have any science-based understanding of how the brain works, but maybe I've added enough color that you can understand what the experience feels like.
Of course they wouldn't suddenly "get it" entirely like in the movies, but I think it would have to be somewhat interesting to see their reaction to going from absolute confidence in their perceptions and knowledge, to.....well, whatever you call the state one is in after having had such experiences. I know for me, even being fairly experienced, returning to a psychedelic state is rather shocking....it seems like it is literally impossible to store even remotely proper memories of it in one's mind, at least mine. Ineffable doesn't seem like the right word for it.
People also tend to forget that ordinary life is crazy complicated in its own right. We don't have trouble remembering it because our brains have tuned itself to compress and operate on those kinds of experiences symbolically.
But since we don't have appropriate symbolic representation for 'deep experience' it gets shoved out of mind before we can form memories.
This is my armchair theory on it. I imagine someone smarter than I has speculated on it, but I've yet to encounter anything on the subject.
I'd also like to read anything on comparisons of the two from people who are experienced in both, although I suspect interactions between the two may skew things a bit.
I understand experiencing something yourself can be a very easy/efficient way for humans to learn. But the ability to transfer knowledge and understanding in other ways even for complicated thoughts is one of the things that sets us apart from lesser beings on this planet.
Don't get me wrong, I understand there are effects. If alcohol weakens myelin and thus boosts unusual interactions between neurons (my layman understanding based on little education on the topic) it might be a good tool to boost creativity, within reason and with a bunch of asterisks attached. Meditation helping you to understand and control your mental state sounds very useful.
But yeah, for psychedelic I've not yet encountered a convincing elevator pitch of it providing lasting benefits beyond being an interesting experience. At least benefits in areas I consider myself lacking. At the same time I've read enough about the AI control problem that messing around with your thinking should only be done with a lot of caution. And an online personality I follow had a shroom trip, including a limited existential crisis and following panic attacks. Just that seems like a high price to pay, considering I don't see it having made him a better person.
So yeah, I'll hold off on such an experience until I get a plausible lecture from some psychedelic advocate or at least encounter statistical evidence of it being beneficial.
I really did have the sense that I was somehow seeing my thought process. As the wiki says:
> At the lower end of level 8B geometry, the experience manifests itself as being able to perceive the supposed organization and structure behind one's current conscious thought stream. This is typically presented in the form of a complex, multisensory, and fast-moving network that contains innately understood and relevant geometric representations of specific and abstract concepts. The experience of these innately understandable geometric representations consistently triggers one to visualize and physically feel the concept through highly detailed conceptual thinking.
> At the higher end of level 8B geometry, the effect retains its lower levels but expands itself to include the experience of subjectively perceiving, through innately understandable geometric representations, the architecture of subconscious neurological processes which are usually outside of one's normal daily perception or understanding. These processes are often interpreted to include concepts such as the structure of one's neurology, memories, perspectives, emotions, and general cognitive functions.
Er no, we do perceive the third due to having stereoscopic vision.
If you had true 3D/volumetric vision, you would find painting over objects aesthetically pointless, because you see behind not just the paint, but also through every layer and sub-component of the object all at once.
For example, most "3D" video games would seem very strangely empty and hollow to a being that could perceive volumetric space directly, because games are implemented by manipulating (many) fundamentally 2D surfaces in 3D space. This implementation technique works to suspend our disbelief because we don't see 3D volumes, we see 3D surfaces.
I would also be very keen to know if the human brain could directly perceive a volumetric space.
Also the concept of perceptual extension is interesting, feed in a bunch of additional information and present it in a consistent way until the brain begins to incorporate it in it's world model. e.g. add additional senses.
The visual system has evolved in a 3D world, in vision science actually the human visual system is considered "2.5D". I don't think we can "visualize" higher dimensions even though we can reason and extrapolate about them just fine.
But with five or more dimensions, it's too tedious and unworkable. So I end up guessing a lot about what projections are useful. It's like that story about blind people trying to perceive an elephant.
Anyway, just thought I'd ask.
That guy who looks like David Spade with a brain tumor on Ancient Aliens will be all over this.
The article is super interesting. I'm just enjoying imagining how someone will tie this to the great pyramid of Giza.
One of the fascinating oddities I learned from that period is that several different founding mothers of Wicca — Valiente and Farrar come to mind — met people who thought the rituals they has created around and soon after WW2 were actually thousands of years old.
I can’t put the connection into words, but it feels like this is related to “Joy in the Merely Real”: https://www.lesswrong.com/posts/x4dG4GhpZH2hgz59x/joy-in-the...
Plus a dash of the way a beginner can totally misunderstand words of art and invent their own totally inaccurate understanding of what’s going on.
> A version of this story was first published in June 2017.
It seems like they just reposed it and added "back in..." It would be more honest if they would just have "news from the past years section". Trying to sneak old articles as news in the front page is bad form.
regarding "dimension" it's used in this sense of dimension of a simplex:
> Following the conventions in algebraic topology, we refer to directed cliques of n neurons as directed simplices of dimension n-1 (which reflects their natural geometric representation as (n-1)-dimensional polyhedra) (see Figure S2; Section 4.1.3). Correspondingly, their sub-cliques are called sub-simplices.
Figure S2 is in the Supplemental Material (and extra PDF 15 page of bonus materials) https://www.frontiersin.org/articles/10.3389/fncom.2017.0004...
Also related def'n on wikipedia: https://en.wikipedia.org/wiki/Simplex#Algebraic_topology
From what I understand of simplex of dim n-1 == clique of n neurons (in a directed graph) https://www.math.ucdavis.edu/~daddel/linear_algebra_appl/App...
> "Networks are often analysed in terms of groups of nodes that are all-to-all connected, known as cliques. The number of neurons in a clique determines its size, or more formally, its dimension," the researchers explained in the 2017 paper.
Can anyone give me a coherent summary of what this (both the quoted paragraphs and the entire article) is trying to say?
Surely you must be trolling ;)
spoiler alert: in math and physics, the dimension of a tensor is simply the dimension of your space, i.e. the number of basis vectors, and the number of indices is called the order (also degree or rank) while datamonkeys on MatrixBurp or TensorFart call the latter the "dimension" and the former ... the ... euh depth? So just like many here are objecting on the usage of "dimension" in the submitted article, (s)he is trolling the very same practice many ML people do with respect to mathematicians and physicists regarding the "dimension" of a tensor.
so in math or physics terminology an 11-dimensional rank 2 tensor would take up just 11 ^ 2 = 121 values, while a 2-dimensional rank 11 tensor would take up 2 ^ 11 = 2048 values.
https://en.wikipedia.org/wiki/M-theory
Simulation much?