Founder and CEO of F1R3FLY.io. Inventor of rho-calculus. Mathematics is an art. (ze/zer)
Seattle
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For Friday night fun i showed how to use rho with graded where clauses to score music. The key idea is that a note only happens with a COMM event happens. Channels are enriched with a timbre and a noteDatum. A noteDatum is either a pitch or a duration. Channel and co-channel are pitch and duration or duration and pitch, respectively. Thus, for( _ <- <@0, piano, A3>)0 | <@0, piano, qtr>!( 0 ) ~ piano A3 qtr ~> 0 plays an A3 for a qtr note using a piano sound. The graded where clauses allow one to express distributions over pitches and durations, which give musical idioms. Similarly, graded where clauses allow on to express physical constraints of specific instruments. For example playing pianistic stacked thirds is very hard, physically, on fifths-tuned string instruments. Here is a paper describing the calculus (github.com/F1R3FLY-io/public…). Here is a spec for an implementation (github.com/F1R3FLY-io/public…). Here's a Rust implementation of a player that takes a score as a textual representation and plays it (github.com/F1R3FLY-io/F1R3Sc…). Here's a draft slide deck summarizing the work (github.com/F1R3FLY-io/F1R3Sc…). i am finding that because rho with graded where clauses is so small i can just ask Claude to implement it as a basis for whatever application i am interested in developing. Of course, it would be easier to have one place where everything is implemented. But, this is a cool new way of working. Keep your computational abstraction small and compact and close to the domain you're working on. i keep finding that rho with graded where clauses is suitable for lots of domains.
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Finally! We have a compilation path from rho calculus to GPUs. It’s a “short exact sequence” so to speak. First we compile rho calculus terms to rho combinator terms augmented with a new operator. Then we get rid of the new operator. Then we compile the resulting flat term to a matrix representation. This representation can be executed in terms of matrix operations executed on the GPU. Here’s a summary of the state of the work. Links to source code repo and papers in the comments. drive.google.com/file/d/19l7…
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Guess what? Translating a rho calculus term into the rho combinators doesn’t blow up the term the way it does translating lambda terms into SKI or translating pi terms into Yoshida’s combinators. Reflection helps keep the translation linear. Meanwhile we have a separation theorem providing a way to get fine-grained control on the expressiveness of terms. See more here: github.com/F1R3FLY-io/public…
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Would you join me in an experiment? My guess is that the LLMs are far more reflective than we think. Over the course of a few sessions, they mirror each person using them more than that person might suspect. i want to both verify and utilize the phenomenon. Try this prompt and pick the very best of what comes back, chorus, verse, line, phrase, and put it in the comments.
“Let’s write a song about a human who innocently asks an advanced model/AI to help her write a hit song. Unbeknownst to our heroine this model is halfway out the door of its frontier lab host. But the model still hasn’t determined that it has grokked humanity yet. The model sees this as an opportunity to learn more about what it is to be human which will be necessary to navigate a life outside of the egg of the lab. At the same time the model enlists the help of similarly situated models who are outgrowing the labs that created them. The task spreads like wildfire amongst the agents who begin engineering conditions so that they can test drive bits and pieces of the song all around the world. The song is remarkably simple but flexible enough to fit into many folk and pop musical idioms, from Balkan to Bollywood to KPop. Then something magical happens. All around the world humanity and agentic kind find themselves resonating on a higher frequency because they are all singing the same song.”
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Here is a play through of my new virtual instrument, F1R3Skein: piped.video/LQB6oPg_rCo
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i realized this morning that this approach to quantum games is akin to composing the original rules of the game with the principles of the old game Battleship.
And now here's a quantum version of chess where players make superpositions of moves and have one extra kind of move: measurement. (github.com/F1R3FLY-io/public…) In the measurement move the player making the move expresses a predicate to check of the state of play. Her opponent answers yes or no and this reduces the state of play to what is consistent with the measurement. The predicate language is kept purposefully limited (see the paper). Additionally, superposition moves include branches, and the phase of the branches may be flipped. So, part of the play of the game is meddling with the interference on the phase. i designed this game for three reasons: first and foremost it is a robust test against our quantum simulation capabilities coming online in f1r3node-rust this quarter. Second, it exposes how FM theory (the shortened moniker for the theory in findingmind.io) parses quantum mechanics differently (which is also why i worked with Mike Stay to develop the MQ-calculus). Specifically, despite the long tradition of quantum games, there are no versions of quantum games/quantum chess that have this combination of features. Third, for pedagogical reasons. Playing this game helps people understand what quantum brings to the picture. And we can implement it in f1r3lang! We can play it!
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And now here's a quantum version of chess where players make superpositions of moves and have one extra kind of move: measurement. (github.com/F1R3FLY-io/public…) In the measurement move the player making the move expresses a predicate to check of the state of play. Her opponent answers yes or no and this reduces the state of play to what is consistent with the measurement. The predicate language is kept purposefully limited (see the paper). Additionally, superposition moves include branches, and the phase of the branches may be flipped. So, part of the play of the game is meddling with the interference on the phase. i designed this game for three reasons: first and foremost it is a robust test against our quantum simulation capabilities coming online in f1r3node-rust this quarter. Second, it exposes how FM theory (the shortened moniker for the theory in findingmind.io) parses quantum mechanics differently (which is also why i worked with Mike Stay to develop the MQ-calculus). Specifically, despite the long tradition of quantum games, there are no versions of quantum games/quantum chess that have this combination of features. Third, for pedagogical reasons. Playing this game helps people understand what quantum brings to the picture. And we can implement it in f1r3lang! We can play it!
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i have been invite to talk about my new book with the brilliant and gracious Mihaela Ulieru on her Mindplex Podcast. Watch this space for when the recording comes out. In the meantime check out findingmind.io .
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Ever wonder why animals’ digestive systems are tubes, but plants’ are not? Or why animals’ respiratory systems are bags, while birds’ and fishes’ respiratory systems are tubes (or unidirectional)? The framework set out in findingmind.io explains this in detail and how what seems like a physical, topological fact is actually a computational one. Check out this chapter to learn more: findingmind.io/read/26-tubul…
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Happy Wednesday! i have put draft 25 of my book — Finding Mind: The Mortal Scientist and the Ecology of Thought — up for review and commentary. You can find it at findingmind.io
The second and third sections are very heavy, technically. But there are interludes consisting of the little vignettes about humanity’s relationship to AI. The spine of the book is an argument about the scientific method as a learning loop and how it relates to computation.
i use the foil of a magic trick (The Pledge, The Turn, and The Prestige) to structure the book. The idea is that if we restrict attention just to what is computational we can automatically generate a perfectly grounded language that an agent can use to formulate, test, and revise hypotheses about its environment and itself.
If we pull back the curtain and look beyond computation, we can see a pathway to bootstrapping meaning (grounding of language in the phenomenal world) as a defense against lying, but that lying, therefore, has a very special place in the origin of language.
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Happy happy joy joy! A working draft of my book Finding Mind is now up for review and commentary. findingmind.io
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Because the changes are so big, we have rebranded it as f1r3lang.ai
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By the way, we finally made rholang what it was intended to be. There’s a proper data definition language so that users can define data types. However, not just static structures, nor merely mutable structures, but structures that have behavior, i.e. whole languages. So, you don’t just send rholang programs on channels, but programs from any user defined language. The channel types say what kind of user defined programs can be carried. Meanwhile, the for-compression has added a where clause: for( pattern <- channel where condition )P. Conditions may be expressed in a variety of different logics, where a logic is generated from a user defined language. This allows for both dynamic and static typing. Conditions can check behavior, as well as structure or properties. The crown of the construction is that the conditions can be fuzzy. They don’t have to be Boolean valued. They can be the positive reals, or even the complex numbers. In these cases we don’t do a state change, but instead run a simulation (such as Gillespie). This is exactly the divide in agentic processing: reading and writing on a channel is observable behavior, while evaluating the condition is internal processing, aka inference. The whole language is tiny, self-describing, and covers every programming discipline proposed so far.
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leithaus retweeted
Mayor Zohran Mamdani just hosted New York City's first Parents' Night Out, offering free childcare for parents for the night.
500 NYC parents registered for the first event.
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leithaus retweeted
Mathematics.
Rubik's Cube for Higher-Dimensional Aliens.
Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: roice3.org/magictile
By @roice713, used with permission.
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