Posting something like this in 2026: they must not have heard of LLMs.
And also: this is such a typical thing a functional programmer would say: for them code is indeed a specification, with strictly no clue (or a vague high level idea at most) as to how the all effing machine it runs on will actually conduct the work.
This is not what code is for real folks with real problems to solve outside of academic circles: code is explicit instructions on how to perform a task, not a bunch of constraints thrown together and damned be how the system will sort it out.
And to this day, they still wonder why functional programming almost never gets picked up in real world application.
Author here: not only have I heard of LLMs but I built a domain-specific programming language for prompt engineering: https://github.com/Gabriella439/grace
It's the best circuit simulator, whose creators did pretty much everything right with the following exceptions:
- using the wrong key for undo
- failing to understand that open-sourcing their baby would have made it 10 times better and 10 times more popular. But when you grow up in the hardware world, these concepts are very, very hard to understand.
In a fews sentences: the evolution of a physical system (quantum and classical) can very successfully be modeled as a stochastic process, and ...
1. state of the system is a real-valued "vector" (could be a vector of with continuous indices), or to put it another way, a "point" in state space.
2. system evolution is described by a real-valued "matrix" (matrix in quotes because it is also possibly a matrix with continuous indices), defined by the laws physics as they apply to the system
3. evolution of the system is modeled by repeatedly applying the matrix to the system (to the vector), possibly with infinitesimal steps.
The major discovery Jacob made is that, historically, folks working on stochastic processes had restricted themselves to studying "markovian" stochastic processes, where the transformation matrix has specific mathematical properties, and this fails to be able to properly model QM.
Jacob removes the constraint that the matrix should obey markovian constraints and lands us in an area of maths that's woefully unexplored: non markovian stochastic processes.
The net result though: you can model quantum mechanics with simple real-valued probabilities and do away entirely with the effing complex numbers.
The whole thing is way more intuitive than the traditional complex number based approach.
Jacob also apparently formally demonstrates that his approach is equivalent to the traditional approach.
This was a good discussion on the topics involved as well; between Jacob Barandes & Tim Maudlin. Though I don't recommend watching this without first getting some familiarity with Barandes's ideas... while there's some explanatory dialog in this video I'm posting, mostly is a discussion. It's nice to see the ideas (politely) challenged and answered.
I'm not sure why you're okay with matrices but not the complex numbers. The complex numbers are a particular kind of matrix. Matrices and vector spaces (especially beyond the normal 3 dimensions) are even more mysterious. Complex numbers are fairly typical, and intuitive (rotations in space).
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