Ciro Santilli @cirosantilli 35

Implementations:

The bioinformatics database: www.ncbi.nlm.nih.gov/

Here's a good example of what you can get out of it: E. Coli K-12 MG1655

It seems impossible to avoid the signaling server. With signaling server:

Games:

Gridworld version of DeepMind Lab.

Open sourced in 2020: analyticsindiamag.com/deepmind-just-gave-away-this-ai-environment-simulator-for-free/

A tiny paper: arxiv.org/pdf/2011.07027.pdf

Very similar to gvgai, Julian Togelius actually called them out on that: DeepMind Lab2D vs gvgai.

TODO get running, publish demo videos on YouTube.

The Dirac equation can be derived basically "directly" from the Representation theory of the Lorentz group for the spin half representation, this is shown for example at Physics from Symmetry by Jakob Schwichtenberg (2015) 6.3 "Dirac Equation".

The Diract equation is the spacetime symmetry part of the quantum electrodynamics Lagrangian, i.e. is describes how spin half particles behave without interactions. The full quantum electrodynamics Lagrangian can then be reached by adding the $U(1)$ internal symmetry.

As mentioned at spin comes naturally when adding relativity to quantum mechanics, this same method allows us to analogously derive the equations for other spin numbers.

Bibliography:

Ciro's best quotes selected by no one other than Ciro can be found at: Ciro Santilli's best random thoughts.

Jesus has some nice ones: Section "Quote by Jesus".

Related to technology:

Analogous to a linear form, a bilinear form is a Bilinear map where the image is the underlying field of the vector space, e.g. ${\mathbb{R}}^n\times {\mathbb{R}}^m\to \mathbb{R}$.

Some definitions require both of the input spaces to be the same, e.g. ${\mathbb{R}}^n\times {\mathbb{R}}^n\to \mathbb{R}$, but it doesn't make much different in general.

The most important example of a bilinear form is the dot product. It is only defined if both the input spaces are the same.