On 1 February 1871 Charles Darwin wrote about these publications to Joseph Hooker, and set out his own speculation that the original spark of life may have been in a "warm little pond, with all sorts of ammonia and phosphoric salts,—light, heat, electricity &c present, that a protein compound was chemically formed". Darwin explained that "at the present day such matter would be instantly devoured or absorbed, which would not have been the case before living creatures were formed." [1]
as far as I understand it, turing completeness is a weaker property than combinatory completeness, which Craig's theorem is addressing. The nonexistence of a singleton combinatory basis doesn't necessarily imply the nonexistence of a turing complete combinator.
Looking forward to hearing about how you're using Opus 4.5, from my experience and what I've heard from others, it's been able to overcome many obstacles that previous iterations stumbled on
Formalization of many of the ideas from HoTT are currently happening in the Agda community. [1] It's out of my wheelhouse, so I don't know the exact motivations, but Agda is apparently a better way to formalize those ideas than in Lean.
Also, there's a new textbook coming out later this year that's a more modern update to the original HoTT book [2] which also has an Agda formalization. [3]
From my brief reading of it, it seems like the interesting bit here is the development of the Hypercatalan numbers as the coefficients of the infinite sums of roots of polynomials. Some partial results for special cases of the Catalan numbers and roots had been found in the past, but the full understanding of the structure they call the Geode enabled generalization of the previous findings.
Have been using Suno over the last few iterations and can vouch for this; steering the final product with style tags is a lot better now and I can use more natural language rather than trying to come up with what the genre specific "wordings" for certain styles of music would be. Good to know the tip about the brackets in lyrics too.
Some examples of style descriptions I've used that generated results close to what I had in mind are "romantic comedy intro music, fast and exciting, new york city" (aiming for something like the Sex and the City theme) and "mature adult romance reality tv show theme song, breakbeats, seductive, intimate, saxophones, lots of saxophones" which did indeed produce cheesy porn music.
I had one of these as a kid; the slow way it drew the graphics onto the screen [1] for a new activity was an aesthetic in itself, like a coloring book being drawn and colored in before your eyes, a perfect loading screen for kids.
Wikipedia notes: The system will "draw" images by filling in areas of the screen with color one line at a time; it is not known whether this is an effect employed for the student's enjoyment or if it is due to the slow processing time of the system.
I'm also self published. I would rather a thousand people steal and read and interact with and talk about my work than to be able to eat selling it to a privileged few. The free software movement is a parallel example of this viewpoint.
The economic reality of today is that words and publishing are cheap. If you have something to say and need to get the word out to as many people as possible, that's wonderful. If you need to eat, then accept this is how it is and write for an audience that's willing to pay you for your work even if it's available for free.
Programs like this and VCV Rack are great ways to get started on the road to building your own modular synthesizer [1]. Many of the modules in the program are based on real hardware, and while the hardware versions of these modules can cost hundreds of dollars, the software versions are using the exact same firmware. Whether you stay virtual or go out and build the hardware equivalent of your rack, it's a great way to experiment and learn the basics at a lower cost than in the past.
Thank you for taking the time to clean this up and release it. I've never played DD Poker, but have experienced the loss of other games when servers go down and the software stops being updated.
I realize source releases aren't always possible, so it's a great gift to the community when one can make it happen and they put in the effort to do so.
> I'm wondering if aphantasia is merely the inability to induce sensory hallucinations at will.
I have aphantasia and this is how I'd define it for myself. I have visual dreams and sometimes when I'm tired or on certain drugs I experience visualizations, but not being able to call these visualizations to mind deliberately I feel is what sets my experience apart from others.
I only have visual aphantasia though and can imagine sounds in my head quite well (with verification of this through being a musician and being able to play by ear), so the effect is definitely not universal and can be limited to certain senses.
Studies have shown that GMs have better mental recall of actual board positions, but if you set the pieces randomly on the board in ways that may be illegal or nonsensical, their recall falls to average. It may be that they're not directly interacting with the visualization, but some mixture of it combined with their knowledge of the position to reconstruct the details.
BespokeSynth takes the concept of a modular synthesizer and expands it so that the application is less just a synth and more a complete modular DAW. I've used it to create MIDI/audio workflows that I couldn't get exactly the way I wanted in Ableton or FL Studio. It also has a module for doing livecoded audio processing in Python that I'm just starting to scratch the surface of.