I have a blog post that links this to the axiom of identity. A=A&!A!=A.
On Fri, 11 Jun 2021, 09:23 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=eyJlcnJvciI6bnVsbCwiYmxvZ19pZCI6MTM3MTA1NDE4LCJibG9nX2xhbmciOiJlbiIsInNpdGVfaWRfbGFiZWwiOiJqZXRwYWNrIiwiZW1haWxfbmFtZSI6ImVtYWlsX3N1YnNjcmlwdGlvbiIsIl91aSI6Mzc0Nzg3MiwiZW1haWxfaWQiOiJiYjI0YmQwYTQwZjE3YTRlY2EzZmU5OGQwNzBkZmE3YSIsImRhdGVfc2VudCI6IjIwMjEtMDYtMTAiLCJsb2NhbGUiOiJlbiIsImN1cnJlbmN5IjoiVVNEIiwiY291bnRyeV9jb2RlX3NpZ251cCI6IlVTIiwiZG9tYWluIjoiYmxvZy5vcGVuY29nLm9yZyIsImZyZXF1ZW5jeSI6IjAiLCJkaWdlc3QiOiIwIiwiaGFzX2h0bWwiOiIxIiwiYW5jaG9yX3RleHQiOiJNYW5hZ2UgU3Vic2NyaXB0aW9ucyIsIl9kciI6bnVsbCwiX2RsIjoiXC94bWxycGMucGhwP3N5bmM9MSZjb2RlYz1kZWZsYXRlLWpzb24tYXJyYXkmdGltZXN0YW1wPTE2MjMzNjkzNDIuNjM5NCZxdWV1ZT1zeW5jJmhvbWU9aHR0cHMlM0ElMkYlMkZibG9nLm9wZW5jb2cub3JnJnNpdGV1cmw9aHR0cHMlM0ElMkYlMkZibG9nLm9wZW5jb2cub3JnJmNkPTAuMDAxNCZwZD0wLjAwNDImcXVldWVfc2l6ZT00JmJ1ZmZlcl9pZD02MGMyYTY3ZTlhY2VlJnRpbWVvdXQ9MTUmZm9yPWpldHBhY2smd3Bjb21fYmxvZ19pZD0xMzcxMDU0MTgiLCJfdXQiOiJ3cGNvbTp1c2VyX2lkIiwiX3VsIjoibGluYXN2IiwiX2VuIjoid3Bjb21fZW1haWxfY2xpY2siLCJfdHMiOjE2MjMzNjkzNDYzMzAsImJyb3dzZXJfdHlwZSI6InBocC1hZ2VudCIsIl9hdWEiOiJ3cGNvbS10cmFja3MtY2xpZW50LXYwLjMiLCJibG9nX3R6IjoiMCIsInVzZXJfbGFuZyI6ImVuIn0&_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. 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