computing with space open notebook
I came back to the The Problem of a Noncommutative BCH formula, related to groups with dilations. It is also related to Curvature via Metric Profiles. See also arXiv:1206.3093. Read also about linearization of self-similar groups by dilations structures (2007) and the related generalized Tits alternative. I took some examples, where there are lots of Continue reading Noncommutative…
I had time to read Terry Tao slides Mathematics in the age of AI. As I write this, it is late and I m in a state of mind which is preparing for sleep. Such a state may (or may not) be favorable to intuition jumps. Therefore here are my first impressions, in such a state, Continue reading Accumulation of state is now cheap
I know this open notebook is useful, though it should be read and accessed together with other sources. [Added: of course the best idea would be to collaborate and test.] For almost any source there are local versions, which are accessible directly, therefore in case of access problems you can turn to those. First, to Continue reading Chorasimilarity knowledge graph and sources
Today I learned that an english translation of Felix Klein s Erlangen Program is on arXiv. Klein is an arXiv author, like for example Leonhard Euler. I save a local copy of this great piece of mathematics, which impressed me since a very long time.
UPDATE: The chemSKI with tokens was updated with informations about UPIM. Soon there will be available, for educational purposes, a description of the UPIM graph rewrites and as well simulations of all structures proposed in the UPIM project, by using the available (local template) Chemlambda-js: a javascript library for graph-rewriting systems like chemlambda and interaction Continue reading More…
Temporary update: a day later, ChatGPT and Gemini chatbots claim that they can t access the content of the post, while Qwen chatbot can access it. It is the first time when I see this behaviour. This update is temporary and it will be removed when this behaviour changes. some hours later I tried again, Continue reading LLM token billing vs chemSKI with tokens
UPDATE: The chemSKI with tokens was updated with informations about UPIM. Soon there will be available, for educational purposes, a description of the UPIM graph rewrites and as well simulations of all structures proposed in the UPIM project, by using the available (local template) Chemlambda-js: a javascript library for graph-rewriting systems like chemlambda and interaction Continue reading…
This is a hand extended to you, be more clever than some of your colleagues in the past. I have reasons to believe that some version of chemlambda chemistries is actively developed in relation with AI. UPDATE: I add this update here, for your information. Here is what I think: that there is a primitive Continue reading Some version of chemlambda AI
From the original page: We explain the BETA rewrite, as a limit of the SHUFFLE rewrite, which appeared for the first time in Pure See, Emergent rewrites. In that source we find the depiction: We shall follow a similar convention of drawing, but we shall look at everything from the point of view of dilations Continue reading The beta rewrite in hexagon form
This is a list of articles, from the oldest to the newest roughly, concerning the path from dilatation structures (or dilation structures) to emergent algebras, to graphic lambda calculus, to em. There is still the need for a contemporary, uniform exposition, but now after the subject proven to be fertile, I suggest reading or mining Continue reading From dilatation structures to emergent algebras…
In the following you see the most common words of lenght at least 6, in the decreasing order of frequency, from the independence announcement of arXiv. It almost makes sense, it conveys the overall meaning. I only added some new lines, to parse it into almost phrases. Here is it: arxiv s scientific nonprofit Simons Foundation Continue reading arXiv July 1st independence announcement, sorted by…
via . I use From [1] definition 2.1, the axioms of a mobi algebra, rewritten, are: I mark this for future use. See also the more recent arXiv:2410.22345 Reconstructing Classical Algebras via Ternary Operations.
The International Mathematical Union (IMU), more precisely the IMU Executive Committee and its Committee on Publishing (CoP) decided to endorse The Leiden Declaration on Artificial Intelligence and Mathematics. I commented that commercial AI is a threat to the publishing and rewards system in mathematics. In the Leiden Declaration there is a (weird) mixture of this Continue reading A CAPTCHA for…
Continues Tetrad playground. In emergent algebras / dilation structures appear approximate operations (last time here appeared in this post) which we prove they satisfy approximate associativity and other laws, with the property that when epsilon tends to 0, they converge to exact laws. In the framework of tetrad for groups, we can arrange these operations Continue reading Emergent algebras tetrad
Moravec s paradox is also true in mathematics. Computation is simple but state can be arbitrarily complex. That is why there is not much value to restrict everything to state and preservation of state. Further I am not going to touch social problems like rejection of AI, enthusiastic slaves of commercial AI, the end of mathematics Continue reading Moravec s paradox in mathematics
It will be useful to have a simpler playground than hexagon. The tetrad seems fit for this purpose. (See also the appearance of torsors.) Recall that a group is an associative quasigroup. Therefore we have a set X with an operation denoted multiplicatively. The operation is one of a quasigroup if for any two elements Continue reading Tetrad playground
Source: Leiden Declaration on Artificial Intelligence and Mathematics. UPDATE 05.06.2026: This is a picture from this source, which shows some mathematicians who participated to the meeting where the Leiden Declaration emerged. Also I found an equally sunny post titled End of Civilization News, where you can find a link to a post on X which Continue reading Leiden Declaration: commercial AI is a…
UPDATE: Yes, this goes back full circle to the beginnings of chemlambda, Quantomatic and NTC vs TC discussions. See for more closely related to the subject Ponto, Shulman (2011) and Reich 2014. It is my supposition that what Scholze is asking for is not exactly this, but I migh project my previously expressed bias. In Continue reading What about a graphical calculus for the six-functor formalism?
Three issues of Mathematics and Mechanics of Solids (MMS) appeared, without the addition of the apology letter of the chief editor David Steigmann, concerning the article Symplectic Bipotentials. See Comments on Symplectic Bipotentials arXiv:2602.14614. See the chronology in The unfolding story of Symplectic Bipotentials. As explained in the Comments, there are two articles which are Continue…
When I try to communicate scientifically, I use a mixture of drawings and mathematical text. Even animations. This is not because I popularize an abstract subject, which can be economically expressed with text only. The rising wave of AI can be helpful in many ways. Related to mathematics, olympiad problems and combinatorics are more of Continue reading A list of radically different AI tasks
UPDATE 31.05.2026: I publish this again, after it was reverted to draft, because there are interesting comments to the recent post at Shtetl-Optimized, as well as more news after the one discussed here. There is much excitement about the Open AI model who disproved an old conjecture in combinatorics. This comes after several similar advances Continue reading Mathematics, birds, frogs and the AI…
[Note for an essay on Madame Bovary: The Cathedral and the Hospital versus The Cathedral and the Bazaar.] More than a month passed since the chief editor of MMS sent me his letter of apology concerning the publication of the unoriginal Symplectic Bipotentials. [sources: chronology, arXiv:2602.14614] After this time, the letter of the editor still Continue reading Emma Bovary, academic editors,…
Sources of programs in awk, js, haskell, python, where if there are local sources (other than github for example), you have links to them, because they are more updated or more interesting than the otherwise available (github for example) ones. [Main source: lambdalife and look at page source ] Also, highly recommended: most programs in js Continue reading Lambdalife: chemlambda programs sources
This is to clarify further some notations used in the hexagon posts, or in Pure See. First, let s look at a hexagon diagram. This is a graph with 6 nodes. The nodes are red or black, 3 of each type. They are numbered from 1 to 6. Each node has 3 ports, marked by the Continue reading Hexagons, trigrams, codons
The post A Directed Interaction Combinators Challenge 3: hexagonal rewrites ended with the following conclusion. The remarkable thing is that all these formalisms [ie Interaction Combinators, SKI calculus, lambda calculus, chemlambda, differential calculus] have the same form, under the more and more general frame SHUFFLE LINEAR FANOUT which we encountered from the first Continue reading…
What I consider significant to read for the chemically inspired computation branch, and also how it started from research in pure mathematics. Still intermediary stage. [Source: lambdalife] EDIT: This is to be seen as a pure Open Science project. It is a side result of the computing with space program. As you know, I would Continue reading Lambdalife: chemlambda notebooks, articles, presentations
Because seems hard to follow to hexagon, here is an intermediary phase, for your convenience [source: lambdalife]. EDIT: to continue the trend from the last posts how can I call it? disclosures? clarifications? this subject also has some weird histories in the background, like this, this or this or this. Quine graphs in Continue reading Lambdalife: interactive chemlambda experiments
Continues after A Directed Interaction Combinators Challenge 2: lateral thinking. It is further continued with Duplication confusion in hexagonal form. We leave aside the problem that the conversion from Interaction Combinator (IC) to chemlambda directed Interaction Combinators (dirIC) looks to be recursive (we use GAMMA on both sides). First of all, once we convert the Continue reading A Directed…
UPDATE 17.04.2026: For the future oriented, here go to hexagon and the yet unexploited AI senescence, as well as to my professional pages at IMAR, lambdalife and my RAAR Lab. As a complement of Marius Buliga’s articles on arXiv with local copies, here are some of my articles from the 1990s. My first published paper Continue reading Some of my articles from past century explain why I went Open…
Continues after the last post: Symplectic bipotentials: the letter of the editor-in-chief. UPDATE Apr 21 2026: Comments on Symplectic Bipotentials, arXiv:2602.14614 are now at version 2, with the abstract This is a reaction to the article Symplectic bipotentials, in published form [2] Harakeh M, Ban M, de Saxce G. Symplectic bipotentials. Mathematics and Mechanics of Continue reading Symplectic…
This is a 2026 update of The Internet can be your pet (2015), produced by Qwen 3.6. See also (local, playable) Chemlambda for the people Biological equivalents of frontier model infrastructure Updated: April 2026 Scope: Verified benchmarks only Providers: OpenAI, Anthropic, Google, Meta, Microsoft Critical Note: This analysis converts verified/synthesized estimates of Continue reading Microfauna:…
This answers to the update put on top of A Directed Interaction Combinators Challenge. The translation between IC and dirIC is actually a translation between nodes and edges. In this image we see that not only the DELTA and GAMMA nodes are translated to A-L and FI-FOE nodes, but also pairs of half edges are Continue reading A Directed Interaction Combinators Challenge 2: lateral thinking
Continuing The unfolding story of Symplectic Bipotentials, further exchanges with the editor-in-chief of the journal Mathematics and Mechanics of Solids, part of Sage Publishing, resulted in the following surprising outcome about the article [1] which plagiarizes my prior work as explained in [2]. The editor prepared and sent me the following pdf letter, which I Continue reading Symplectic…
UPDATE: The challenge holds, but it is more funny that is suggested here. Can you see why? I ll come back to this: see part 2. In (local, playable) arXiv:2005.06060 Artificial life properties of directed interaction combinators vs. chemlambda is described a realization of Lafont Interaction Combinators IC by using the chemlambda chemistry dirIC and Continue reading A Directed Interaction…
I remembered this and thought is important to mention, for the readers who are bored by the dispute around symplectic bipotentials. The much discussed uncited reference [10] arXiv:1902.04598 is not only the first appearance in a proof of symplectic bipotentials, but also covers for the first time unilateral contact. As a consequence any minimization algorithm Continue reading A note on…
UPDATE 26 Mar 2026: Continues with Symplectic bipotentials: the letter of the editor-in-chief This post is made to host the discussion after the stage where the expert of the MMS journal writes that I m right, but on the other side the report makes many verifiable false assertions too (see further). Previously: The timeline of the Continue reading The Symplectic bipotentials story: conclusion
This post continues The unfolding story of Symplectic Bipotentials. It is followed by The Symplectic bipotentials story: conclusion. The editor of Mathematics and Mechanics of Solids just sent me the report of the journal expert, after two weeks, when my arXiv:2602.14614 appeared. I share the report with you, here. After the report, I put my Continue reading Continuation of the Symplectic…
Right after I wrote Enough fun: conclusion, an unexpected sequence of updates appeared, around the publication of the article Symplectic bipotentials on 03 Feb 2026, by the journal Mathematics and Mechanics of Solids, a part of Sage Publishing, which plagiarizes my prior work. This post serves as a host of those updates and also for Continue reading The unfolding story of Symplectic Bipotentials
Edit Feb 22 2026: The many updates to this post, including links and quotes, moved to the next, more recent The unfolding story of Symplectic Bipotentials. The goal of the last posts was partially explained in Enough fun? , but for the casual reader it is not completely clear what is happening here. There was a Continue reading Enough fun: conclusion
COMMENT: This subject appeared here in several places, among them the post Curvdimension and curvature of a metric profile III. See also the research proposal for IHES named Non-euclidean analysis start-up which was written about the same time as the paper [2] and as the research described in the recent post Heisenberg Group Geometry and Continue reading Curvature via Metric Profiles
UPDATE: There is now a 4th post along the same ideas described here. Despite the post Rearrangement, I continued to add three (update: now four) more generated posts, which are actually serious. These posts are interesting because they clarify things which appeared in this notebook and also kind of add to the explanation of how Continue reading Enough fun?
UPDATE/COMMENT: The inequality from section 6.3 is the most interesting, but in my opinion the geometrical idea is not well understood. The main part of the post is an AI generated explanation (heavily edited for sycophancy, ie removement of various fundamental , profound , etc, 18 mentions of my name), is decently good as an introduction to Continue reading Heisenberg Group Geometry and Hofer…
(updates are at the bottom of the page) Read also The unfolding story of Symplectic bipotentials. The original generated self-sufficient html which is the basis of this post. See the acknowledgement footer for details about generation. AI summarize as a tool for scientists or open peer reviews advances fast, example Mars 2026: the summary of Continue reading Verification of Attribution Claims in…
Based on: M. Buliga, The em-convex rewrite system, arXiv:1807.02058 [cs.LO], 2018. [Added: see also A kaleidoscope of graph rewrite systems in topology, metric geometry and computer science. UPDATE: and a distant answer to Hilbert fifth problem without one parameter subgroups] 1. Geometric Motivation: Beyond Vector Space Tangents In Riemannian geometry, the tangent space at a Continue reading The…
Some recent posts here were reverted to draft and a better version is to be found elsewhere. Why? Because these were educational and also made by curiosity, using some of those LLM which allow free use, without login. In the past I used Phind, Grok, now I used ChatGPT and Qwen. The results were interesting, Continue reading Rearrangement
Required reading: In [3] is thrown a challenge, to make Chemical Joy or chemJoy, which would be the chem- equivalent of Joy (or FORTH). That means an artificial chemistry which implements Joy, like chemSKI is an artificial chemistry which implements SKI. But, it is mentioned, without the need to stay in an 1 dimensional stack. Continue reading Forsp syntax of lambda calculus, a hint for Chemical…
UPDATE: Has door UPDATE: New logo, less verbose: ________________ After my first call for a Random Asymmetric Asemantic Research lab, the RAAR lab appeared and is now under development. The readers of this blog know that I like to make a symbolic start with a logo, here is it: and here is the link to Continue reading The RAAR AI lab has a logo
UPDATE: A truly local version as part of my homepage. I think all of arXiv content should be free to browse and search, for humans or programs. Remember that a year ago arXiv announced: Attention arXiv users: arXiv mirrors to shut down September 15th, 2024. (archived) That is why here is the content of my Continue reading Marius Buliga s articles on arXiv with local copies
Here the content of the post Same thing is reframed in hexagon style. There are two conjugated notions, the chora and the derivative, which can be seen as knot diagrams or as pure see like trigrams, now we ll see them as hexagons. Let s start with the derivative. In trigrams notation this is defined as and Continue reading Same thing in hexagonal form
In A shuffle rewrite in the limit was proposed a modification of the SH24 rewrite, in the sense that the LHS pattern transforms into the RHS pattern where the one of the common edge decorations changes. (Then we passed to the limit with mu). The remark is that the new edge decoration has the expression Continue reading A shuffle rewrite in the limit (2)