Moyo, My reply was perhaps too short. I can give very precise and exact descriptions of how all this relates to fractals and tilings ... If you prod me, I can supply details. A very important, key bridge to this is understanding is the work of Przemyslaw Prusinkiewicz at Algorithmic Botany -- http://algorithmicbotany.org/papers/ -- and the easiest way to understand that is to go in historical order, reading the earliest papers first. I believe the work there is nothing short of mind-blowing, and stunningly important, yet is curiously very under-appreciated, for some unclear reason.
--linas On Fri, Jun 11, 2021 at 3:01 PM Linas Vepstas <[email protected]> wrote: > Similar ideas have been circulating for decades or longer. Yes, the > concept of fractals and tilings are similar. My goal here is to point out > that these ideas can be implemented in software. I'm trying to drum up the > practical conversation, the one of "how can we do this?" . > > On Fri, Jun 11, 2021 at 2:24 AM Tofara Moyo <[email protected]> wrote: > >> This is interesting. I came across similar ideas too and i posted them on >> the AGI facebook page last year june. here they are for comparison. >> >> >> this post is about the way things repeat and change in the world. in >> short something repeats for a while , such as you passing houses while you >> are walking down a road. So you pass house after house...then you get to an >> intersection and there are no more houses, but after that you then find >> that the thing that repeats is "passing houses AND intersections"...so you >> group the houses with the intersection and you pass this new grouping many >> times before you get to a mall, then you group all three things together >> and you keep walking past this new grouping untill you get outside the >> city, then you group the city and the country side and you start passing >> many cities and country sides as you go, then this becomes counries and >> continents and planets and solar systems and galaxies...in short this >> process describes reality, from the way a piece of wood bark is rough to >> the way we even think >> >> in mathematics there is a topic called fractals that describes shapes >> that look the same at different scales,here is a fractal shape that looks >> the same even when you zoom in. So as you walk past houses , think of that >> as zooming in to different scales and finding the same object you started >> with, house after house represents scale after scale. this is more >> complicated however because after the first set of scales we change focus, >> and then zoom in on this new grouping/focus as if that was the fractal.... >> >> There are other type of fractal like shapes or at least objects that >> follow the principle that are more applicable to this. Called tilings. >> These are tiles or identical shapes that are placed side by side and fill a >> space with no gaps in between them. So the steps you take while walking >> would each be a tile , while when you stop that becomes a tile of a >> different shape from the stepping tiles that you join to them...then this >> new grouping of tiles becomes the shape that you are tiling, when this >> changes you tile the combination of the change with the original tiles. >> this is a multi shape tiling that is binary in nature. Even the stepping >> tiling can be broken into two different tiles, one for each leg...and so on. >> >> A meriology is something that is made of parts. A chair is made of parts >> that are made of parts all the way down to atoms and even further. the >> parts of a chair are separated by space and time. The parts of the tiling >> above may be seperated by space and time such as walking or the texture of >> a surface, but it can also be seperated by something even stranger. think >> of the tiling where you are left handed while everyone else is right >> handed. What separtes the lefties as a group from the righties. it cant be >> the normal space or time as they are not litteraly seperated by a >> demarcation placed somewhere. If we could specify a type of space that >> these two tiles are filling wouldnt that simply be a conceptual space? and >> if we were to tile a space with concepts would that not be thinking? So we >> already have a way to use this in AI. >> >> >> >> On Fri, Jun 11, 2021 at 2:33 AM Linas Vepstas <[email protected]> >> wrote: >> >>> I just wrote up a new blog post on ... well, the usual topic. I'm cc'ing >>> the Link Grammar mailing list, as it has been instrumental in waking me to >>> these ideas. >>> >>> -- Linas >>> >>> ---------- Forwarded message --------- >>> From: OpenCog Brainwave <[email protected]> >>> Date: Thu, Jun 10, 2021 at 6:55 PM >>> Subject: [New post] Everything is a Network >>> To: <[email protected]> >>> >>> >>> Linas Vepstas posted: "The goal of AGI is to create a thinking machine, >>> a thinking organism, an algorithmic means of knowledge representation, >>> knowledge discovery and self-expression. There are two conventional >>> approaches to this endeavor. One is the ad hoc assembly of assorted" >>> >>> New post on *OpenCog Brainwave* >>> <https://blog.opencog.org/?author=5> Everything is a Network >>> <https://blog.opencog.org/2021/06/10/everything-is-a-network/> by Linas >>> Vepstas <https://blog.opencog.org/?author=5> >>> >>> The goal of AGI >>> <https://en.wikipedia.org/wiki/Artificial_general_intelligence> is to >>> create a thinking machine, a thinking organism, an algorithmic means of >>> knowledge >>> representation >>> <https://en.wikipedia.org/wiki/Knowledge_representation_and_reasoning>, >>> knowledge >>> discovery <https://en.wikipedia.org/wiki/Knowledge_extraction> and >>> self-expression >>> <https://en.wikipedia.org/wiki/Natural_language_generation>. There are >>> two conventional approaches to this endeavor. One is the ad hoc assembly of >>> assorted technology pieces-parts, >>> <https://www.youtube.com/watch?v=y_oem9BqUTI> with the implicit belief >>> that, after some clever software engineering, it will just come alive. The >>> other approach is to propose some grand over-arching theory-of-everything >>> that, once implemented in software, will just come alive and become the >>> Singularity <https://en.wikipedia.org/wiki/Technological_singularity>. >>> >>> This blog post is a sketch of the second case. As you read what follows, >>> your eyes might glaze over, and you might think to yourself, "oh this is >>> silly, why am I wasting my time reading this?" The reason for this is that, >>> to say what I need to say, I must necessarily talk in such generalities, >>> and provide such silly, childish examples, that it all seems a bit vapid. >>> The problem is that a theory of everything must necessarily talk about >>> everything, which is hard to do without saying things that seem obvious. Do >>> not be fooled. What follows is backed up by some deep and very abstract >>> mathematics that few have access to. I'll try to summon a basic >>> bibliography at the end, but, for most readers who have not been studying >>> the mathematics of knowledge for the last few decades, the learning curve >>> will be impossibly steep. This is an expedition to the Everest of >>> intellectual pursuits. You can come at this from any (intellectual) race, >>> creed or color; but the formalities may likely exhaust you. That's OK. If >>> you have 5 or 10 or 20 years, you can train and work out and lift weights. >>> You can get there. And so... on with the show. >>> >>> The core premise is that "everything is a network >>> <https://en.wikipedia.org/wiki/Network_theory>" -- By "network", I mean >>> a graph <https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)>, >>> possibly with directed edges, usually with typed >>> <https://en.wikipedia.org/wiki/Type_theory> edges, usually with >>> weights, numbers, and other data on each vertex or edge. By "everything" I >>> mean "everything". Knowledge, language, vision, understanding, facts, >>> deduction, reasoning, algorithms, ideas, beliefs ... biological >>> molecules... everything. >>> >>> A key real-life "fact" about the "graph of everything" is it consists >>> almost entirely of repeating sub-patterns. For example, "the thigh bone >>> is connected to the hip bone <https://en.wikipedia.org/wiki/Dem_Bones>" >>> -- this is true generically for vertebrates >>> <https://en.wikipedia.org/wiki/Vertebrate>, no matter which animal it >>> might be, or if it's alive or dead, it's imaginary or real. The patterns >>> may be trite, or they may be complex. For images/vision, an example might >>> be "select all photos containing a car >>> <https://en.wikipedia.org/wiki/CAPTCHA>" -- superficially, this >>> requires knowing how cars look alike, and what part of the pattern is >>> important (wheels, windshields) and what is not (color, parked in a lot or >>> flying >>> through space <https://where-is-tesla-roadster.space/live>). >>> >>> The key learning task is to find such recurring patterns, both in fresh >>> sensory input (what "the computer" is seeing/hearing/reading right now) and >>> in stored knowledge (when processing a dataset - previously-learned, >>> remembered knowledge - for example, a dataset of medical symptoms). The >>> task is not just "pattern recognition >>> <https://en.wikipedia.org/wiki/Pattern_recognition>" identifying a >>> photo of a car, but of pattern discovery >>> <https://en.wikipedia.org/wiki/Frequent_pattern_discovery> -- learning >>> that there are things in the universe called "cars", and that they have >>> wheels and windows -- extensive and intensive properties. >>> >>> Learning does not mean "training >>> <https://en.wikipedia.org/wiki/Training,_validation,_and_test_sets>" -- >>> of course, one can train, but AGI cannot depend on some pre-existing >>> dataset, gathered by humans, annotated by humans. Learning really means >>> that, starting from nothing at all, except one's memories, one's sensory >>> inputs, and one's wits and cleverness, one discovers something new, and >>> remembers it. >>> >>> OK, fine, the above is obvious to all. The novelty begins here: The best >>> way to represent a graph with recurring elements in it is with "jigsaw >>> puzzle <https://en.wikipedia.org/wiki/Jigsaw_puzzle> pieces". (and NOT >>> with vertexes and edges!!) The pieces represent the recurring elements, and >>> the "connectors" on the piece indicate how the pieces are allowed to join >>> together. For example, the legbone has a jigsaw-puzzle-piece connector on >>> it that says it can only attach to a hipbone. This is true not only >>> metaphorically, but (oddly enough) literally! So when I say "everything is >>> a network" and "the network is a composition of jigsaw puzzle pieces", the >>> deduction is "everything can be described with these (abstract) jigsaw >>> pieces." >>> >>> That this is the case in linguistics has been repeatedly rediscovered by >>> more than a few linguists. It is explained perhaps the most clearly and >>> directly in the original >>> <https://www.cs.cmu.edu/afs/cs.cmu.edu/project/link/pub/www/papers/ps/tr91-196.pdf> >>> Link >>> Grammar >>> <https://www.cs.cmu.edu/afs/cs.cmu.edu/project/link/pub/www/papers/ps/LG-IWPT93.pdf> >>> papers, although I can point at some other writings as well; one from a >>> "classical" >>> (non-mathematical) humanities-department linguist >>> <https://www.academia.edu/36534355/The_Molecular_Level_of_Lexical_Semantics_by_EA_Nida>; >>> another from a hard-core mathematician - a category theorist - who >>> rediscovered this from thin air >>> <http://www.cs.ox.ac.uk/people/bob.coecke/NewScientist.pdf>. Once you >>> know what to look for, its freakin everywhere. Say, in biology, the Krebs >>> cycle <https://en.wikipedia.org/wiki/Citric_acid_cycle> (citric acid >>> cycle) - some sugar molecules come in, some ATP goes out, and these >>> chemicals relate to each other not only abstractly as jigsaw-pieces, but >>> also literally, in that they must have the right shapes >>> <https://en.wikipedia.org/wiki/Molecular_recognition>! The carbon atom >>> itself is of this very form: it can connect, by bonds, in very specific >>> ways. Those bonds, or rather, the possibility of those bonds, can be >>> imagined as the connecting tabs on jigsaw-puzzle pieces. This is not just >>> a metaphor, it can also be stated in a very precise mathematical sense. (My >>> lament: the mathematical abstraction to make this precise puts it out of >>> reach of most.) >>> >>> The key learning task is now transformed into one of discerning the >>> shapes of these pieces >>> <https://github.com/opencog/atomspace/blob/master/opencog/sheaf/docs/sheaves.pdf>, >>> given a mixture of "what is known already" plus "sensory data". The >>> scientific endeavor is then: "How to do this?" and "How to do this quickly, >>> efficiently, effectively?" and "How does this relate to other theories, >>> e.g. neural networks >>> <https://en.wikipedia.org/wiki/Artificial_neural_network>?" I believe >>> the answer to the last question is "yes, its related", and I can >>> kind-of explain how >>> <https://github.com/opencog/learn/blob/master/learn-lang-diary/skippy.pdf>. >>> The answer to the first question is "I have a provisional way of doing >>> this <https://github.com/opencog/learn>, and it seems to work >>> <https://github.com/opencog/learn/blob/master/learn-lang-diary/connector-sets-revised.pdf>". >>> The middle question - efficiency? Ooooof. This part is ... unknown. >>> >>> There is an adjoint task to learning, and that is expressing and >>> communicating. Given some knowledge, represented in terms of such jigsaw >>> pieces, how can it be converted from its abstract form (sitting in RAM, on >>> the computer disk), into communications: a sequence of words, sentences, or >>> a drawing, painting? >>> >>> That's it. That's the meta-background. At this point, I imagine that >>> you, dear reader, probably feel no wiser than you did before you started >>> reading. So what can I say to impart actual wisdom? Well, lets try an >>> argument >>> from authority <https://en.wikipedia.org/wiki/Argument_from_authority>: >>> a jigsaw-puzzle piece is an object in an (asymmetric) monoidal category >>> <https://en.wikipedia.org/wiki/Monoidal_category>. The internal >>> language of that category is ... a language ... a formal language >>> <https://en.wikipedia.org/wiki/Formal_language> having a syntax >>> <https://en.wikipedia.org/wiki/Syntax>. Did that make an impression? >>> Obviously, languages (the set of all syntactically valid expressions) and >>> model-theoretic >>> theories <https://en.wikipedia.org/wiki/Model_theory> are dual to >>> one-another (this is obvious only if you know model theory). The learning >>> task is to discover the structure >>> <https://en.wikipedia.org/wiki/Model_(model_theory)>, the collection of >>> types <https://en.wikipedia.org/wiki/Type_(model_theory)>, given the >>> language <https://en.wikipedia.org/wiki/Text_corpus>. There is a wide >>> abundance of machine-learning software that can do this in narrow, specific >>> domains. There is no machine learning software that can do this in the >>> fully generic, fully abstract setting of ... jigsaw puzzle pieces. >>> >>> Don't laugh. Reread this blog post from the beginning, and everywhere >>> that you see "jigsaw piece", think "syntactic, lexical element of a >>> monoidal category", and everywhere you see "network of everything", think >>> "model theoretic language". Chew on this for a while, and now think: "Is >>> this doable? Can this be encoded as software? Is it worthwhile? Might this >>> actually work?". I hope that you will see the answer to all of these >>> questions is yes. >>> >>> And now for a promised bibliography. The topic both deep and broad. >>> There's a lot to comprehend, a lot to master, a lot to do. And, ah, I'm >>> exhausted from writing this; you might be exhausted from reading. A >>> provisional bibliography can be obtained from two papers I wrote on this >>> topic: >>> >>> - Sheaves: A Topological Approach to Big Data >>> >>> <https://github.com/opencog/atomspace/blob/master/opencog/sheaf/docs/sheaves.pdf> >>> - Neural-Net vs. Symbolic Machine Learning >>> >>> <https://github.com/opencog/learn/blob/master/learn-lang-diary/skippy.pdf> >>> >>> The first paper is rather informal. The second invoked a bunch of math. >>> Both have bibliographies. There are additional PDF's in each of the >>> directories that fill in more details. >>> >>> This is the level I am currently trying to work at. I invite all >>> interested parties to come have a science party, and play around and see >>> how far this stuff can be made to go. >>> *Linas Vepstas <https://blog.opencog.org/?author=5>* | June 10, 2021 at >>> 11:55 pm | Categories: Uncategorized >>> <https://blog.opencog.org/?taxonomy=category&term=uncategorized> | URL: >>> https://wp.me/p9hhnI-cl >>> >>> Comment >>> <https://blog.opencog.org/2021/06/10/everything-is-a-network/#respond> >>> See all comments >>> <https://blog.opencog.org/2021/06/10/everything-is-a-network/#comments> >>> >>> Unsubscribe >>> <https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=https%3A%2F%2Fsubscribe.wordpress.com%2F%3Fkey%3Da9a418716d1b232b4d6f1b1829be75ae%26email%3Dlinasvepstas%2540gmail.com%26b%3DIuFxBBRYbGv3Hprjfcb1nN1xTFHgj5HkuY-x-lT6QKxqkZMgov9AM8QuMvodMCGn32Q3oTFW0et24AFIz1oCUdSZiyQlYOmTn36q6nLoKLLJow%253D%253D&sr=1&signature=674cb680ce749d47971c3d661d17cd4d&user=3747872&_e=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&_z=z> >>> to no longer receive posts from OpenCog Brainwave. >>> Change your email settings at Manage Subscriptions >>> <https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=https%3A%2F%2Fsubscribe.wordpress.com%2F%3Fkey%3Da9a418716d1b232b4d6f1b1829be75ae%26email%3Dlinasvepstas%2540gmail.com&sr=1&signature=ece1c66e405464c8308b765ebceb3f20&user=3747872&_e=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&_z=z>. >>> >>> >>> *Trouble clicking?* Copy and paste this URL into your browser: >>> https://blog.opencog.org/2021/06/10/everything-is-a-network/ >>> >>> >>> >>> -- >>> Patrick: Are they laughing at us? >>> Sponge Bob: No, Patrick, they are laughing next to us. >>> >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "opencog" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to [email protected]. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/opencog/CAHrUA34gQSDZnbkV1Mp7aEOSGoENOkQTAZoBBRVL6%3DwJWfJv%3DA%40mail.gmail.com >>> <https://groups.google.com/d/msgid/opencog/CAHrUA34gQSDZnbkV1Mp7aEOSGoENOkQTAZoBBRVL6%3DwJWfJv%3DA%40mail.gmail.com?utm_medium=email&utm_source=footer> >>> . >>> >> -- >> You received this message because you are subscribed to the Google Groups >> "opencog" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/opencog/CAFMxUd-PQnKC5-PfFQV1pJ3jRe1Y773nHzaL%2BcgtDUZQv5ypfQ%40mail.gmail.com >> <https://groups.google.com/d/msgid/opencog/CAFMxUd-PQnKC5-PfFQV1pJ3jRe1Y773nHzaL%2BcgtDUZQv5ypfQ%40mail.gmail.com?utm_medium=email&utm_source=footer> >> . >> > > > -- > Patrick: Are they laughing at us? > Sponge Bob: No, Patrick, they are laughing next to us. > > > -- Patrick: Are they laughing at us? 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