I wrote: Fantasy magic and “real” magic are closer than you think. Mathematically speaking, the Kabbalic tree of life is a tree in the same sense as a perk tree in Skyrim where the ontological basis doesn’t necessarily have to describe a vector of reality for prima facie, they are just “empty symbols” where they are given semantic meaning. To say it a different way, you can algorithmically traverse the tree of life whether or not you believe it to be real, so you can deduce that the relations are consistent and formulas derived from those relations are true regardless Read More
I wrote: Gaffluence wrote: Does the first law of Thermodynamics apply to magical energies too? The law being that, energy cannot be created or destroyed, only transformed (simplified version). The answer is no. Conservation of energy is due a temporal translation invariance as described in Noether’s theorem and the Lagrangian. Energy conservation is a consequence of invariance under time translations. Something more abstract than time would not be beholden to that invariance and thus would not be conserved. Basically, if it is not physical, it would not be temporal, and if it is not temporal, it is not beholden Read More
Linear Algebra is a text for a first US undergraduate Linear Algebra course. You can use it as a main text, as a supplement, or for independent study. It is Free. The book, the complete answers to all exercises, classroom presentation slides, and a lab manual using Sage, are all available for download, as well as for purchase. The third edition incorporates many suggestions sent by users, including many more beginning exercises, and a new Topic on coupled oscillators and eigenvalues.
SageMath is a computer algebra system with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics. SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers. Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.