This is going to be used by woo woo types for years. Did you know that our brains operate in 11 dimensions? Or, how can we get our brains to operate in all the dimensions it's capable of? Or, brains operate in 11 dimensions...and the soul makes up the other seven. Seven? That's a spiritual number. Etc...
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.
You're right, it is, but there's a lot of woo surrounding it and a lot of videos floating around with wild eyed people exaggerating the power of neuroplasticity.
I wonder what is the underlying urge behind the woo purveyors. There is more than a lifetime’s worth of weird trippy stuff that is 100% legit. There’s no need to muddy the waters; mystery abounds in the real world.
I was briefly interested in woo as a teenager — Wicca, telekinesis, shapeshifting, that sort of thing.
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.
> 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.
At the lab the other day we were discussing hyperparameter optimization in deep learning and visualizing N-dimensions spaces. Since all structures are Trees, which can be encoded in Tree Notation, we think there is a new type of visualization that can leverage that to easily visualize N-dimensional spaces.
From the number of times I've seen it mentioned, there seems to be very little that Tree Notation isn't in some way related to. But for the life of me I can't figure it out.
From the examples it seems like a newline deliminated text format that uses spaces for indentation with indentation levels representing nested structure. Which seems fine enough but I feel like I'm missing some sort of philosophically profound implication of this format or something.
> From the number of times I've seen it mentioned, there seems to be very little that Tree Notation isn't in some way related to. But for the life of me I can't figure it out.
Change the word "Tree Notation" to "binary Notation". What we discovered is that there is a remarkably simple notation that is all you need for representing abstractions and higher level languages.
Just as Leibniz in the 1600's discovered that all you need is 0 and 1 to represent all information, we discovered that all you need is trees to represent all structures(and tree notation -- the most minimal way to encode trees), that has profound implications, just like binary.
Think about all the things you use that depend on binary. All of the systems that depend on our modern will programming languages, Tree Notation will make all of those systems better in the decades ahead.
People will say this is just "S-Expressions". Exactly! Except S-Expressions done correctly! When you try to reduce S-Expressions to perfection, you get Tree Notation. If you know S-Expressions and you still don't get that, this might help: https://medium.com/@breckyunits/removing-the-2s-from-trinary...
You should read "Zen and the art of motorcycle maintenance", it a autobiography of a man who develops a meta-physical system existing of the holy trinity of a thing, the representation of a thing and the essence this representation is missing. Don't read it for the theory but the slow decent into madness.
No I mean "we". This is a huge collaborative effort. We wouldn't be getting anywhere if not for the help of many dozens (more like hundreds, at this point) people helping out.
> "Zen and the art of motorcycle maintenance"
I have that book, I can't remember reading it, however. Thanks for the rec. I'll give it another look.
> Don't read it for the theory but the slow decent into madness.
The reason why you see my name everywhere and no one else's is merely because of comments like this. I have very thick skin and can take it, but I don't want to subject my friends and collaborators to this kind of gaslighting. We are almost at the point where the evidence is overwhelming that this theory is correct, and we have peer-reviewed papers in the works (with dozens of collaborators with fancy edu positions whose full names will be on the paper), and then it's game over. In the meantime you can either look at the increasing piles of extraordinary evidence (for example, I made a language today called Dumbdown in less than an hour http://treenotation.org/designer/#standard%20dumbdown that I would not be surprised if a variant evovles to be bigger than markdown) and think about things for yourself, or jump to a (wrong) conclusion simply because this is a low probability/black swan/outlier event.
I don't know man, I like those parens. They turn basically any text editor into a basic structural editor. Commands like Vim's % can jump to the matching paren easily, and pretty much all programmer text editors have a feature to highlight the matching paren.
So to me it's not a matter of subjective taste but rather pragmatism. S-expressions are just easier to edit.
The examples linked in the FAQ 404 and all of the "whats" would better be titled "why's" as there is very little explanation of what the heck Tree Notation actually is just a bunch talking about what it can represent.
It's syntax error free but syntax includes whitespace, does that mean you just hid all syntax errors inside the semantics errors bucket?
In what exact ways is tree notation more base than all the other notations that make it such a strong choice?
It's mentioned it can't map 1:1 to JSON/XML, if it's just words and nodes at an offset why not?
Tree notation could be the greatest thing since sliced bread but the pages on the website do nothing to help me understand what it actually is just that it's great.
> there is very little explanation of what the heck Tree Notation
The docs are weak, but resources are limited. Ideally people will start their own sites/blogs/etc where they try to explain Tree Notation in their own words. All of the questions you have below are answered in many places (people have had hundreds+ of questions, so I do my best to answer them but I'm not doing a great job at organizing these -- the Faq, gihtub, papers, and subreddits are helping, but ideally other people will start to create content).
> It's syntax error free but syntax includes whitespace, does that mean you just hid all syntax errors inside the semantics errors bucket?
Just like there are no errors in binary, there are no errors in tree notation. Tools can operate on binary without understanding the semantics. Tools can operate on tree notation without understanding the semantics. This is very powerful. If you have experience writing tools that parse/edit/generate code, it should click. If you don't, try building some stuff that does using some existing techniques and tools from parsing, grammar, and compiler theory and then give Tree Notation a shot. There still are errors at the Tree Language level, but they become much easier to handle and fix.
> In what exact ways is tree notation more base than all the other notations that make it such a strong choice?
All of the other notations listed have both syntax errors and semantic errors. Tree notation eliminates the entire category of syntax errors.
> It's mentioned it can't map 1:1 to JSON/XML, if it's just words and nodes at an offset why not?
Subtle details, but certain properties of those languages (like XML's dual attributes/tags axes) or higher level constructs (Tree Notation does not have a concept of "number" you need a higher level Tree Language for that) prevents the direct mapping unless you use a higher level Tree Language.
> Tree notation could be the greatest thing since sliced bread but the pages on the website do nothing to help me understand what it actually is just that it's great.
I agree. Help wanted! Anyone is welcome to build their own sites about Tree Notation and/or contribute pull requests to the docs and repos.
The docs are more than weak, for something that's supposed to take over the world in 2 years I can't even click half the links in the FAQ?
> Just like there are no errors in binary, there are no errors in tree notation.
You can make any format "no errors" with little effort, the problem is not creating garbage data in the process.
> Tools can operate on binary without understanding the semantics. Tools can operate on tree notation without understanding the semantics. This is very powerful.
And there are infinitely many representations which can take this form. The problem is all such representations are no different than each other. I.e. tree notation can't represent anything binary can't. To actually do anything new you need to understand the syntax so if the main selling point is "are syntax accepts anything" well so does a million others before and after. The question isn't "how can generic encoding work" it's "what does Tree Notations syntax do that others don't already".
> All of the other notations listed have both syntax errors and semantic errors. Tree notation eliminates the entire category of syntax errors.
But they aren't eliminated at all they are just hidden to produce garbage later on instead. In S-expressions if I randomly drop a parenthesis I have mismatched syntax. In Tree Notation if I randomly drop a newline I have some completely different piece of data that validly represents garbage. The issue isn't eliminated just because it parses and this isn't the first format that can hold arbitrary data!
.
In the end though what is this beyond yet another form of S-expression? Is there something it does that a simple replacement regex would generate an invalid S-expression? If not why blow smoke up everyone's ass instead of just saying "Tree Notation is a S-expression format that uses whitespace instead of parenthesis"?
> The docs are more than weak, for something that's supposed to take over the world in 2 years I can't even click half the links in the FAQ?
On my goodness. Thank you. Fixed. I have a script that checks for broken links "npx linkinator -r https://treenotation.org" but I must have screwed something up because those were not getting detected. (Nit: 10 years! not 2 ;) )
> You can make any format "no errors" with little effort, the problem is not creating garbage data in the process.
This is a very valid point. But Tree Notation does give you a lot of meaning -- lines/words/scopes -- without knowing the semantics of the Tree Language. But you do have a good argument here that if people don't come to a consensus on even these things, then Tree Notation could just be garbage. There will need to develop a common language for the universal tree notation semantics.
> And there are infinitely many representations which can take this form.
Good point.
> The question isn't "how can generic encoding work" it's "what does Tree Notations syntax do that others don't already".
Tree Notation is the simplest method we can come up with to do all the things are existing syntaxes and languages can do. By simplest, we mean "tree notation will always have fewer or equal pieces in terms of absolute complexity than a different notation for any given task". And our bet is that simplicity of atomic ingredients triumphs in the long run because less costs less.
But the proof is in the pudding. Tree Notation won't really start taking off (if ever) until there is better tooling and some "killer app" new tree languages.
> But they aren't eliminated at all they are just hidden to produce garbage later on instead.
Clinicians are now using Tree Notation to write their medical records on pen and paper (peer reviewed paper coming soon). There's no such thing as syntax errors. Their "code" looks just like S-expressions, with prettified formatting, except without paranetheses. They can have semantic errors using either one (for instance, spelling "dose as does"). But they cannot have syntax errors with Tree Notation. Imagine instead we were instructing them to use S-Expressions--suddenly their notebooks would be filled with syntax errors for missing paranetheses. They would have 0 benefit and all downside by adding parens.
> If not why blow smoke up everyone's ass instead of just saying "Tree Notation is a S-expression format that uses whitespace instead of parenthesis"?
I'm putting a small fortune and an immense amount of effort into this (and giving everything away), because I believe it will eliminate drastic amounts of unnecessary complexity in so many domains all throughout the world, and will indeed, amongst other things, help us cure cancer, which is certainly near and dear to my heart and I'm sure to so many other people on here. I want to make the biggest and boldest statements I can here, so I can get harsh and sharp critical feedback like yours, that is very helpful and can save us time by pointing out flaws (both in theory and practice like the broken links). If this were something for Lispers, I wouldn't care so much (I love lisp, but it would be an incremental improvement). This is for all the people of the world. We are going to simplify and make better code in all domains. It's a mammoth effort that's going to take billions and thousands of smart people. This is just the beginning.
Wat. No, they're not. Counter-example: triangles. Triangles are not trees.
I did, however, notice that you've been spamming all kinds of threads with posts along the lines of "Apropos topic X, Tree Notation will totally revolutionize X. Follow tree-notation-URL to stay up-to-date with Tree Notation, once [if] we ever find a way to explain what makes Tree Notation so different from other notations!"
(where X is a random topic which is mostly or completely unrelated to Tree Notation)
Yes, triangles are trees. Please list your definition of a triangle.
> where X is a random topic which is mostly or completely unrelated to Tree Notation)
What is binary notation related to? Is it related to medicine? It is related to automobiles? Is it related to deep space? Is it related to food? Is it related to government? Try to do any of those things without binary notation. This is a big idea. A very infrequent big idea.
> I'll put the crux of my argument in Trees, which is a rigorous language
Interesting how you're overloading the word "tree" in this context. You're presenting a definition in the format of a tree. And concluding that the resulting object is itself a tree. It's like saying that swords are made of wood, and proving it by carving the definition of a sword into a piece of wood. This is quackery.
Graphs, and trees, have perfectly rigorous definitions. They've been defined in a plurality of rigorous languages. Your "definition" doesn't even mention edges, unless they're implied by "cycleNode" somehow; in either case it appears that your "better" graph theory only contains a single graph of any given order. Graph theorists expect a few more than that.
Just because Mathematics is one of the most rigorous languages we have, does mean it is rigorous. It would be like saying Roman Numerals are not a great language for math. If I say that today no one blinks an eye. But if I said that 2k years ago people would say "Uh huh. Great start...".
Let me define a "rigorous" language.
A rigorous langauge is one which can be defined completely in a single document starting with 0 and 1 and working it's way all the way up to whatever it is you want to prove.
> Graphs, and trees, have perfectly rigorous definitions. They've been defined in a plurality of rigorous languages.
If you can provide a link to a single page that starts with 0 and 1 and builds all the way up to defining "graphs and trees" and how a "triangle is not a tree", then I will agree with you.
> Interesting how you're overloading the word "tree" in this context.
Sorry, that was a typo, I meant to write Tree Notation. I'll fix.
> A rigorous langauge is one which can be defined completely in a single document starting with 0 and 1 and working it's way all the way up to whatever it is you want to prove.
Is there a document like this for your tree notation? Not trying to criticize; I'm legitimately interested to see how this would be done.
You aren't, by any chance, also working on "Time AI"[1], are you? Ya know, that most excellent product demonstrated at BH2019, that fixes the problem that all encryption is now broken due to "quasi-prime" number theory.
I have no idea what that is, but looks interesting.
Tree Notation is free and open and there is no signup form. Just take it and do what you want with it. Play with it, examine it, see how it is built, see how it has evolved, try to find flaws, try to utilize its strengths, monetize it, share it, troll it, whatever you want.
There's no secrecy with Tree Notation. It's all out there.
I clicked the Github link. There was nothing but an incomprehensible pen on notebook sketch there.
My dude, maybe you're on to something clever, maybe you're just chasing your own tail. But until you write down clearly exactly what it is that you're on about, nobody can tell. And then you're just annoying us.
Focus on a single document somewhere that explains enough to make just a few people go "Aha, this can be used for X! I'll contribute!"
Now you have three half-baked "papers" on various stuff, a "data science platform" that I can't figure out how works, and lots of vague fluffy ideas.
This particular comment (on a post about visualizing structures in 11 dimensions) is very much targeted toward a very particular type of person who works in a research lab in deep learning and is familiar with high dimensional visualizations. If you happen to be in that target audience, you might have a glimmer of an idea of what it is about. But otherwise it probably looks like jibberish, I get it.
> Focus on a single document somewhere that explains enough to make just a few people go "Aha, this can be used for X! I'll contribute!"
I'm working with well over 50 different people in many countries at this point helping them with their tree languages and projects. So even if the majority of people don't yet understand what the heck this is all about, enough do that we're starting to make faster progress.
What you are seeing is a lot of data points. 2 years I made a logical argument, but that didn't go very far. Extraordinary claims require extraordinary evidence. Get ready for a deluge of extraordinary evidence.
“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.”
May well turn out later on that AI is best modeled for speed and detail at 11 bit resolution - after all - evolution has done a lot of work that we equate as machine learning.
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.
When the giraffe class was first released it was too OP with its tall neck, allowing it to access food previously unreachable to many other classes while also being able to keep an eye on predators lurking at distance. Upon next evolutionary tick, it had to be nerfed.
> May well turn out later on that AI is best modeled for speed and detail at 11 bit resolution - after all - evolution has done a lot of work that we equate as machine learning.
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.
iirc, back propagation sounds similar in inspection to some of the processes seen in sleeping brains. Ie what they see in MRIs looks like what back propagation might look like from outside. But I’m really not comfortable enough with these terms to speak about them.
The jury is still out on back-propagation (i.e. reverse accumulation automatic differentiation) within the brain (retrograde signalling from the post-synaptic neuron to the pre-synaptic neuron may still be discovered and turn out to approximate RM AD)
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"
"There can't be back-propagation in evolution without biological time-travel of information." You still can't do such time-travel in computers, sure you could simulate it but on a chronological scale in reality, your not time traveling.
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??
> In other words, it has nothing to do with the human brain creating structures in 11 dimensions.
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.
I don't agree. The brain does not create structures in up to 11 dimensions, full stop. This is a popular science article. To use that word from standard vocabulary to describe something that just happens to use the same word as some utterly esoteric mathematical definition is misleading at best. And then to imply that the brain creates such structures is just compounding the problem.
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".
> The brain does not create structures in up to 11 dimensions, full stop.
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.
Words are used for communication. The definition of a word derives from the mutually understood definition of the word between the author and the reader.
>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.
> 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.
> To use that word from standard vocabulary to describe something that just happens to use the same word as some utterly esoteric mathematical definition is misleading at best.
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?
I don’t know about re-writing the findings, but if I was to do so, I’d start with this statement from early in the article:
“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.
> 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.
Time is a valuable commodity, it is disingenuous to trick people into reading articles through the use of clickbait headlines.
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".
> 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?
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.
> 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?
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?
It does create 11 dimensional structures, in the same sense programs can have 11 dimensional arrays. Not at the quantum reality level.
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.
The author points this out explicitly in the article.
“Just to be clear - this isn’t how you’d think of spatial dimensions...”
Pretty great how from lack of gathering information (reading the article) you claim the author is peddling insufficient information.
So tired of the “I am very smart community.”
Go outside and act like a human being. No one cares one bit to read cranky grandpa opinions on every fucking forum post out there.
Good for you, Mr Math. Hey, I got a degree in math. I get it. But knowing these things really means very little. We just know some things a lot of people don’t, and it makes us as special as a bus driver or a dog walker.
It would really be great if there was a Reddit or HN with story and link votes, but no comment sections. Really do not care about everyone else’s hot takes.
It's hard to tell from the post what the terms are being used to describe. First of all, I would consider a dimension either space-time or mathematical to be an orthogonal/independent concern. Now where this gets distractingly blurry is that the paper itself says "The number of neurons in a clique determines its size, or more formally, its dimension." which uses dimension to mean size, like a length.
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.
Why would the space-time and mathematical concept of dimensions be orthogonal? Don't we use the mathematical concept of dimension when dealing with space-time dimensions? Software developers in particular should have intuitive understanding of this connection, because implementing space-time in code is usually done through methods that closely resemble mathematical dimensions. Eg if you were to implement a point in 3 dimensional space time you'd give the point xyz and t as variables.
I don't mean the math one orthogonal to the space-time one. I mean that dimensions are orthogonal to each other whether in math or space-time (except special relativities).
Oh ok, so they actually mean that they found 11-dimensional directed simplices in neuronal connectivity, which then implies the barycentric coordinates describing relative activity levels in the simplex will have 11 dimensions. Simple.
Tangential but I've always thought it may be possible for a human brain to experience higher spatial dimensions, it's just that all it ever experiences is 3. Imagine a video game is designed in 4 spatial dimensions and is fed directly into the brain through a neuralink type interface. The brain is pretty adaptable, would the recipient correctly experience those 4 dimensions?
I've seen more than three dimensions with LSD. At least, I've seen what looks a lot like those rotating hypercube images. Except more complicated, and looking somewhat like Mandelbrot sets.
Extraordinary claims require extraordinary evidence. With your mind in a suggestible state, it's much easier to convince yourself that you're seeing in 4D than is to actually see in 4D.
It's pretty easy to work out what they actually saw from the words used to describe them. A hypercube rotation is a 4d object projected into 3 dimensions. Nothing extraordinary at all about that.
Yes, it was a visual hallucination, and so constrained to two dimensions plus perspective. But I clearly recall the sense that I was seeing a 2D projection of a higher-dimensional image.
Yeah, visualizing 2D/3D shapes is not extraordinary. "The sense" of an extra dimension is meaningless woo, unless someone with sufficient mathematical experience is able to observe consistent properties of a shape's higher-dimensional structure.
It would have to be higher dimensional properties observed by someone who doesn't have mathematical experience relayed to and confirmed by someone who does.
Obviously anything experiential can be dismissed as "meaningless woo", but as someone who's done a fair amount of LSD and is a lifelong skeptic, it's an unmistakable experience that the hallucinations are taking place in a higher ordered space.
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.
I hope some day to encounter a situation where a non-psychedelic-experienced person lecturing the experienced about how silly they are agrees to "put their money where their mouth is" so to speak and actually try it out for themselves, and then return to the previous argument and reflect upon it with the new insight they've gained.
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.
I have a lot of meditation experience, and deep trance states are also extremely hard to hold on to. Meditating on the phenomena has revealed that it's a combination of unfamiliarity with the subject matter along with the sheer complexity of the experience that leads to inability to remember all the details.
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.
> But since we don't have appropriate symbolic representation, our (or, most people's at least) mind is literally unable to store the experience.
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'm not a fan of the "you have to experience it to understand it" mantra.
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.
That's a great wiki. I'm talking about 8A/8B. And it's hard to describe, because you forget most of it so fast. What I remember most vividly is close to the image "Abstract by Matt W. Moore", but not so hard edged. More like "Untitled by Luke Brown". Like a bunch of strings of 3D characters, rotating and writhing through higher dimensions. And they moved and changed so quickly that I could never make out what they meant. Plus the fact that I had virtually no memory left.
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.
Visually we perceive 2 dimensions (i.e. you can't see behind things), the third is just something we imagine as being closer to or further from the camera without being able to directly perceive it. So maybe the fourth would be the same, but just orthogonal to the third.
Stereoscopic vision doesn't let you see a whole 3D scene at once, it just gives some clues as to how far away things are in the 2D scene which you can perceive visually.
You're right that our vision gives us a 3D perception, but only in the same way that a surface in a 3D space may be stretched and squashed and even have discontinuities, but is still fundamentally 2-dimensional, it has no volume. That still doesn't give us volumetric 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.
I'd lika to be able to have a vr app that let's me move in 4D space. I guess at least some kind of sensoring for 4D orientation and 4d acceleration should be developed.
I've been wanting to make a vr application for a while that lets you navigate around n dimensional structures with ability to control which dimensions you are moving in.
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.
That sounds like it would be very interesting. And while we can't extend our senses just yet, we may be able to swap them. I'm very curious if anyone has tried to use a space-filling Hilbert curve to transform vision into audio and let their brain adjust to it like suggested in this video https://youtu.be/3s7h2MHQtxc
Interesting idea. My understanding is that some of the seeing impaired community does use echo location tools to help navigate. There were also some pin grid tests in the past that effectively gave the seeing impaired the ability to see again. Which is one of the things that got me to thinking about interesting ways we could extend our senses.
> it may be possible for a human brain to experience higher spatial dimensions
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.
Personally the best abstraction I've seen for how the brain works is a "pointer and cell machine" similar to how people introduce s-expressions. It works well with how I find myself thinking about lists (like the alphabet) where I have to "cdr" down it to find any of the items.
A cell holds some datum (like "Q" and all its associations) and a pointer is something that can reference another cell, for example ("Q", <rest of alphabet after Q>) includes a pointer to the rest of the alphabet after "Q". This (datum <ptr to the rest>) pair is exactly the LISP list, usually written as s-expressions.
Tangential question: What are good ways to visualize multidimensional data? Excel etc can chart 3D data, but even that is hard because stuff overlaps. And years ago, I had some Excel code that generated 3D views of 4D data.
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.
Use non spatial dimensions as well, like color, size, and shape. You can also use clever projections like t-sne to reduce the number of dimensions while retaining some of the structure of the data (https://www.youtube.com/watch?v=RJVL80Gg3lA)
I know someone with aphantasia who is an excellent mathematician, I asked him what he does instead of visualising and he says that he does mathematics with the kinesthetic feeling of arbitary imaginary limbs. This may possibly explain why he is one of the very few people I know who seems to experience no conceptual jump in difficulty when solving problems that have 4 or more dimensions when compared to solving those with 3 or less.
I thought this straight away. It made me think that the brain's structure has evolved in resonance with the fundamental dimensionality of the universe.
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.
There is a great video serie by infinite series[1] that goes into detail how the neural network of a brain processes information. The way I understand it is that the more abstract thoughts can are represented as higher dimensional structures of a directed graph.
> Just to be clear - this isn't how you'd think of spatial dimensions (our Universe has three spatial dimensions plus one time dimension), instead it refers to how the researchers have looked at the neuron cliques to determine how connected they are.
> "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?
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.
126 comments
[ 5.4 ms ] story [ 183 ms ] threadThat 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.
At the lab the other day we were discussing hyperparameter optimization in deep learning and visualizing N-dimensions spaces. Since all structures are Trees, which can be encoded in Tree Notation, we think there is a new type of visualization that can leverage that to easily visualize N-dimensional spaces.
If you want to see a prototype (or contribute one!) when one is live, you can follow that issue here: https://github.com/treenotation/jtree/issues/35
From the examples it seems like a newline deliminated text format that uses spaces for indentation with indentation levels representing nested structure. Which seems fine enough but I feel like I'm missing some sort of philosophically profound implication of this format or something.
Change the word "Tree Notation" to "binary Notation". What we discovered is that there is a remarkably simple notation that is all you need for representing abstractions and higher level languages.
Just as Leibniz in the 1600's discovered that all you need is 0 and 1 to represent all information, we discovered that all you need is trees to represent all structures(and tree notation -- the most minimal way to encode trees), that has profound implications, just like binary.
Think about all the things you use that depend on binary. All of the systems that depend on our modern will programming languages, Tree Notation will make all of those systems better in the decades ahead.
People will say this is just "S-Expressions". Exactly! Except S-Expressions done correctly! When you try to reduce S-Expressions to perfection, you get Tree Notation. If you know S-Expressions and you still don't get that, this might help: https://medium.com/@breckyunits/removing-the-2s-from-trinary...
You should read "Zen and the art of motorcycle maintenance", it a autobiography of a man who develops a meta-physical system existing of the holy trinity of a thing, the representation of a thing and the essence this representation is missing. Don't read it for the theory but the slow decent into madness.
No I mean "we". This is a huge collaborative effort. We wouldn't be getting anywhere if not for the help of many dozens (more like hundreds, at this point) people helping out.
> "Zen and the art of motorcycle maintenance"
I have that book, I can't remember reading it, however. Thanks for the rec. I'll give it another look.
> Don't read it for the theory but the slow decent into madness.
The reason why you see my name everywhere and no one else's is merely because of comments like this. I have very thick skin and can take it, but I don't want to subject my friends and collaborators to this kind of gaslighting. We are almost at the point where the evidence is overwhelming that this theory is correct, and we have peer-reviewed papers in the works (with dozens of collaborators with fancy edu positions whose full names will be on the paper), and then it's game over. In the meantime you can either look at the increasing piles of extraordinary evidence (for example, I made a language today called Dumbdown in less than an hour http://treenotation.org/designer/#standard%20dumbdown that I would not be surprised if a variant evovles to be bigger than markdown) and think about things for yourself, or jump to a (wrong) conclusion simply because this is a low probability/black swan/outlier event.
Black swans are rare. But they do happen.
So to me it's not a matter of subjective taste but rather pragmatism. S-expressions are just easier to edit.
But I also think the world without parens will be a much better place, once we get there with the tooling and ecosystem.
I don't know how long that will take. 2020 I hope?
It's syntax error free but syntax includes whitespace, does that mean you just hid all syntax errors inside the semantics errors bucket?
In what exact ways is tree notation more base than all the other notations that make it such a strong choice?
It's mentioned it can't map 1:1 to JSON/XML, if it's just words and nodes at an offset why not?
Tree notation could be the greatest thing since sliced bread but the pages on the website do nothing to help me understand what it actually is just that it's great.
The docs are weak, but resources are limited. Ideally people will start their own sites/blogs/etc where they try to explain Tree Notation in their own words. All of the questions you have below are answered in many places (people have had hundreds+ of questions, so I do my best to answer them but I'm not doing a great job at organizing these -- the Faq, gihtub, papers, and subreddits are helping, but ideally other people will start to create content).
> It's syntax error free but syntax includes whitespace, does that mean you just hid all syntax errors inside the semantics errors bucket?
Just like there are no errors in binary, there are no errors in tree notation. Tools can operate on binary without understanding the semantics. Tools can operate on tree notation without understanding the semantics. This is very powerful. If you have experience writing tools that parse/edit/generate code, it should click. If you don't, try building some stuff that does using some existing techniques and tools from parsing, grammar, and compiler theory and then give Tree Notation a shot. There still are errors at the Tree Language level, but they become much easier to handle and fix.
> In what exact ways is tree notation more base than all the other notations that make it such a strong choice?
All of the other notations listed have both syntax errors and semantic errors. Tree notation eliminates the entire category of syntax errors.
> It's mentioned it can't map 1:1 to JSON/XML, if it's just words and nodes at an offset why not?
Subtle details, but certain properties of those languages (like XML's dual attributes/tags axes) or higher level constructs (Tree Notation does not have a concept of "number" you need a higher level Tree Language for that) prevents the direct mapping unless you use a higher level Tree Language.
> Tree notation could be the greatest thing since sliced bread but the pages on the website do nothing to help me understand what it actually is just that it's great.
I agree. Help wanted! Anyone is welcome to build their own sites about Tree Notation and/or contribute pull requests to the docs and repos.
The scope of tools is pretty limited though: compression, encryption, ecc/encoding.
> Tools can operate on tree notation without understanding the semantics. This is very powerful.
GIGO still applies. So you move your errors downstream, as mentioned. The space where this is a win also seems pretty limited.
The docs are more than weak, for something that's supposed to take over the world in 2 years I can't even click half the links in the FAQ?
> Just like there are no errors in binary, there are no errors in tree notation.
You can make any format "no errors" with little effort, the problem is not creating garbage data in the process.
> Tools can operate on binary without understanding the semantics. Tools can operate on tree notation without understanding the semantics. This is very powerful.
And there are infinitely many representations which can take this form. The problem is all such representations are no different than each other. I.e. tree notation can't represent anything binary can't. To actually do anything new you need to understand the syntax so if the main selling point is "are syntax accepts anything" well so does a million others before and after. The question isn't "how can generic encoding work" it's "what does Tree Notations syntax do that others don't already".
> All of the other notations listed have both syntax errors and semantic errors. Tree notation eliminates the entire category of syntax errors.
But they aren't eliminated at all they are just hidden to produce garbage later on instead. In S-expressions if I randomly drop a parenthesis I have mismatched syntax. In Tree Notation if I randomly drop a newline I have some completely different piece of data that validly represents garbage. The issue isn't eliminated just because it parses and this isn't the first format that can hold arbitrary data!
.
In the end though what is this beyond yet another form of S-expression? Is there something it does that a simple replacement regex would generate an invalid S-expression? If not why blow smoke up everyone's ass instead of just saying "Tree Notation is a S-expression format that uses whitespace instead of parenthesis"?
On my goodness. Thank you. Fixed. I have a script that checks for broken links "npx linkinator -r https://treenotation.org" but I must have screwed something up because those were not getting detected. (Nit: 10 years! not 2 ;) )
> You can make any format "no errors" with little effort, the problem is not creating garbage data in the process.
This is a very valid point. But Tree Notation does give you a lot of meaning -- lines/words/scopes -- without knowing the semantics of the Tree Language. But you do have a good argument here that if people don't come to a consensus on even these things, then Tree Notation could just be garbage. There will need to develop a common language for the universal tree notation semantics.
> And there are infinitely many representations which can take this form.
Good point.
> The question isn't "how can generic encoding work" it's "what does Tree Notations syntax do that others don't already".
Tree Notation is the simplest method we can come up with to do all the things are existing syntaxes and languages can do. By simplest, we mean "tree notation will always have fewer or equal pieces in terms of absolute complexity than a different notation for any given task". And our bet is that simplicity of atomic ingredients triumphs in the long run because less costs less.
But the proof is in the pudding. Tree Notation won't really start taking off (if ever) until there is better tooling and some "killer app" new tree languages.
> But they aren't eliminated at all they are just hidden to produce garbage later on instead.
Clinicians are now using Tree Notation to write their medical records on pen and paper (peer reviewed paper coming soon). There's no such thing as syntax errors. Their "code" looks just like S-expressions, with prettified formatting, except without paranetheses. They can have semantic errors using either one (for instance, spelling "dose as does"). But they cannot have syntax errors with Tree Notation. Imagine instead we were instructing them to use S-Expressions--suddenly their notebooks would be filled with syntax errors for missing paranetheses. They would have 0 benefit and all downside by adding parens.
> If not why blow smoke up everyone's ass instead of just saying "Tree Notation is a S-expression format that uses whitespace instead of parenthesis"?
I'm putting a small fortune and an immense amount of effort into this (and giving everything away), because I believe it will eliminate drastic amounts of unnecessary complexity in so many domains all throughout the world, and will indeed, amongst other things, help us cure cancer, which is certainly near and dear to my heart and I'm sure to so many other people on here. I want to make the biggest and boldest statements I can here, so I can get harsh and sharp critical feedback like yours, that is very helpful and can save us time by pointing out flaws (both in theory and practice like the broken links). If this were something for Lispers, I wouldn't care so much (I love lisp, but it would be an incremental improvement). This is for all the people of the world. We are going to simplify and make better code in all domains. It's a mammoth effort that's going to take billions and thousands of smart people. This is just the beginning.
Wat. No, they're not. Counter-example: triangles. Triangles are not trees.
I did, however, notice that you've been spamming all kinds of threads with posts along the lines of "Apropos topic X, Tree Notation will totally revolutionize X. Follow tree-notation-URL to stay up-to-date with Tree Notation, once [if] we ever find a way to explain what makes Tree Notation so different from other notations!"
(where X is a random topic which is mostly or completely unrelated to Tree Notation)
It's quite annoying.
> where X is a random topic which is mostly or completely unrelated to Tree Notation)
What is binary notation related to? Is it related to medicine? It is related to automobiles? Is it related to deep space? Is it related to food? Is it related to government? Try to do any of those things without binary notation. This is a big idea. A very infrequent big idea.
So what are your definitions of tree and triangle?
Mathematics is not a rigorous language, so I'll put the crux of my argument in Tree Notation, which is a rigorous language:
There you go, a triangle is a cycle with length 3. Ergo, a triangle is a tree.typo fix: changed Trees to Tree Notation.
Uh huh. Great start...
> I'll put the crux of my argument in Trees, which is a rigorous language
Interesting how you're overloading the word "tree" in this context. You're presenting a definition in the format of a tree. And concluding that the resulting object is itself a tree. It's like saying that swords are made of wood, and proving it by carving the definition of a sword into a piece of wood. This is quackery.
Graphs, and trees, have perfectly rigorous definitions. They've been defined in a plurality of rigorous languages. Your "definition" doesn't even mention edges, unless they're implied by "cycleNode" somehow; in either case it appears that your "better" graph theory only contains a single graph of any given order. Graph theorists expect a few more than that.
Let me define a "rigorous" language.
A rigorous langauge is one which can be defined completely in a single document starting with 0 and 1 and working it's way all the way up to whatever it is you want to prove.
> Graphs, and trees, have perfectly rigorous definitions. They've been defined in a plurality of rigorous languages.
If you can provide a link to a single page that starts with 0 and 1 and builds all the way up to defining "graphs and trees" and how a "triangle is not a tree", then I will agree with you.
> Interesting how you're overloading the word "tree" in this context.
Sorry, that was a typo, I meant to write Tree Notation. I'll fix.
Is there a document like this for your tree notation? Not trying to criticize; I'm legitimately interested to see how this would be done.
I wish. We have a lot of ongoing threads about it. Someone has one somewhere for logic gates, IIRC.
Here's a snippet from 1 from a conversation the other day on how to build up to an if statement.
Obviously that's not ideal but hopefully some more data on what we are talking about with that.The idea is we'd like to be able to compare 2 systems objectively and decide which is the simpler one.
Here's a rough paper from 2017 (before I had any experience in academia): https://github.com/treenotation/jtree/blob/master/papers/pap...
1) https://m.youtube.com/watch?v=fPMxIt79PkE
Tree Notation is free and open and there is no signup form. Just take it and do what you want with it. Play with it, examine it, see how it is built, see how it has evolved, try to find flaws, try to utilize its strengths, monetize it, share it, troll it, whatever you want.
There's no secrecy with Tree Notation. It's all out there.
My dude, maybe you're on to something clever, maybe you're just chasing your own tail. But until you write down clearly exactly what it is that you're on about, nobody can tell. And then you're just annoying us.
Focus on a single document somewhere that explains enough to make just a few people go "Aha, this can be used for X! I'll contribute!"
Now you have three half-baked "papers" on various stuff, a "data science platform" that I can't figure out how works, and lots of vague fluffy ideas.
> Focus on a single document somewhere that explains enough to make just a few people go "Aha, this can be used for X! I'll contribute!"
I'm working with well over 50 different people in many countries at this point helping them with their tree languages and projects. So even if the majority of people don't yet understand what the heck this is all about, enough do that we're starting to make faster progress.
What you are seeing is a lot of data points. 2 years I made a logical argument, but that didn't go very far. Extraordinary claims require extraordinary evidence. Get ready for a deluge of extraordinary evidence.
“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.
[1]: https://www.youtube.com/watch?v=6xbQ2WbTp0E
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.
https://en.wikipedia.org/wiki/Chemotaxis
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.
“Just to be clear - this isn’t how you’d think of spatial dimensions...”
Pretty great how from lack of gathering information (reading the article) you claim the author is peddling insufficient information.
So tired of the “I am very smart community.”
Go outside and act like a human being. No one cares one bit to read cranky grandpa opinions on every fucking forum post out there.
Good for you, Mr Math. Hey, I got a degree in math. I get it. But knowing these things really means very little. We just know some things a lot of people don’t, and it makes us as special as a bus driver or a dog walker.
It would really be great if there was a Reddit or HN with story and link votes, but no comment sections. Really do not care about everyone else’s hot takes.
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.
https://store.steampowered.com/app/619210/4D_Toys/
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.
https://en.wikipedia.org/wiki/2.5D_(visual_perception)
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.
https://en.wikipedia.org/wiki/M-theory
Simulation much?
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.
[1] https://www.youtube.com/watch?v=akgU8nRNIp0
> "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?
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...