Magarena by Ciro Santilli 37 Updated 2025-07-16
Open source MtG engine implementation written in Java.
Seems to have an option to download art from internet as well.
Ciro Santilli wonders how legal it is. They very explicitly do not mention the words Magic: The Gathering anywhere.
Their UI does a good job at being self explanatory. Space is the shortcut to skip phases.
No online play.
TODO it appears to parse card functionality out of the human readable text! That's genius, as it helps automatically get new cards working, and squirt around legal issues.
Hyperparameter by Ciro Santilli 37 Updated 2025-07-16
A parameter that you choose which determines how the algorithm will perform.
In the case of machine learning in particular, it is not part of the training data set.
Hyperparameters can also be considered in domains outside of machine learning however, e.g. the step size in partial differential equation solver is entirely independent from the problem itself and could be considered a hyperparamter. One difference from machine learning however is that step size hyperparameters in numerical analysis are clearly better if smaller at a higher computational cost. In machine learning however, there is often an optimum somewhere, beyond which overfitting becomes excessive.
For the typical case of a linear form over , the form can be seen just as a row vector with n elements, the full form being specified by the value of each of the basis vectors.
Solution for given and of:
where is the exponential map.
If we consider just real number, , but when X and Y are non-commutative, things are not so simple.
Furthermore, TODO confirm it is possible that a solution does not exist at all if and aren't sufficiently small.
This formula is likely the basis for the Lie group-Lie algebra correspondence. With it, we express the actual group operation in terms of the Lie algebra operations.
Notably, remember that a algebra over a field is just a vector space with one extra product operation defined.
Since a group is basically defined by what the group operation does to two arbitrary elements, once we have that defined via the Baker-Campbell-Hausdorff formula, we are basically done defining the group in terms of the algebra.
Lp space by Ciro Santilli 37 Updated 2025-07-16
Integrable functions to the power , usually and in this text assumed under the Lebesgue integral because: Lebesgue integral of is complete but Riemann isn't
Three-level laser by Ciro Santilli 37 Updated 2025-07-16
The type of laser described at: Video "How Lasers Work by Scientized (2017)", notably youtu.be/_JOchLyNO_w?t=581. Mentioned at: youtu.be/_JOchLyNO_w?t=759 That point also mentions that 4-level lasers also exist and are more efficient. TODO dominance? Alternatives?
Video 1.
Three-level laser system by Dr. Nissar Ahmad (2021)
Source.
Noether's theorem by Ciro Santilli 37 Updated 2025-07-16
For every continuous symmetry in the system (Lie group), there is a corresponding conservation law.
Furthermore, given the symmetry, we can calculate the derived conservation law, and vice versa.
As mentioned at buzzard.ups.edu/courses/2017spring/projects/schumann-lie-group-ups-434-2017.pdf, what the symmetry (Lie group) acts on (obviously?!) are the Lagrangian generalized coordinates. And from that, we immediately guess that manifolds are going to be important, because the generalized variables of the Lagrangian can trivially be Non-Euclidean geometry, e.g. the pendulum lives on an infinite cylinder.
Video 1.
The most beautiful idea in physics - Noether's Theorem by Looking Glass Universe (2015)
Source. One sentence stands out: the generated quantities are called the generators of the transforms.
Video 2.
The Biggest Ideas in the Universe | 15. Gauge Theory by Sean Carroll (2020)
Source. This attempts a one hour hand wave explanation of it. It is a noble attempt and gives some key ideas, but it falls a bit short of Ciro's desires (as would anything that fit into one hour?)
Video 3.
The Symmetries of the universe by ScienceClic English (2021)
Source. youtu.be/hF_uHfSoOGA?t=144 explains intuitively why symmetry implies consevation!

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