“I have the ability to travel from a world with a physical story to a world with the math tools needed to express that story.” “We prefer it that when the Physicist comes looking, needing something, we can tell the Physicist that we already have it.” When you studied Linear Algebra they taught you aContinue reading “The Mad Math Hatter”
Author Archives: Robert Sterling
Ask Alice About Tensors
We want to show you some math that shows what is necessary if you wish to go down the rabbit hole to find Invariancy. After that, we want to be brutally honest about the consequences of the choices we made to get Invariancy. We will even show the story from an angle that indicates theContinue reading “Ask Alice About Tensors”
Macondo and Tensors
Components of a white rank 4 tensor (identified by coordinates such as 1122) convert a blue 2×2 matrix to a red 2×2 matrix.
A Military Example of Tensor Invariance under Coordinate Transformation
“Sir, they are coming from the West. They’re heading directly East, they’re heading straight toward us!” “What is their vector?” “Thirty kilometers per hour. They have 10 km to go. They will be here in 20 minutes. What do you want us to do?” “Rotate the coordinate system 90 degrees counter-clockwise. That will move eastContinue reading “A Military Example of Tensor Invariance under Coordinate Transformation”
A Game of Decoding a Boolean Algebra
Suppose you had some basic knowledge of Propositional Logic and Venn Diagrams. Suppose you knew that there were three operators in Boolean Algebra (AND, OR, NOT) and two symbols for true and false. You know what AND, OR and NOT do, it’s just that you are used to seeing them with different symbols. Assume thatContinue reading “A Game of Decoding a Boolean Algebra”
Commutation of Multiplication
Commutation of Multiplication is the rule that says “a*b = b*a”. Commutation of Multiplication is an axiom. We don’t claim that we can prove it from our collection of starting rules, rather, it is one of the rules in our collection of starting rules. However, we at Mockingbird Academy maintain that there is a wayContinue reading “Commutation of Multiplication”
Space
If you search for information about space, in the context of math, you will find articles written about specific types of space, and often the choice is Vector Space. It is as if it is not possible to talk about a general Space. We will take a stab at it in Appendix B, but pleaseContinue reading “Space”
Vectors in Math
The math used to develop tensors begins with vectors. The study of vectors takes us to several places where we encounter basics such as Linearity and several Identities of Algebra. Vectors are used in Physics when we deal topics such as Velocity, Acceleration and Force.
Food and Scalars
Well, when you make a recipe you use numbers, and you might want to double the size of the recipe because several guests are coming over, and so you scale the recipe by doing Scalar Multiplication, using the scalar 2. We might use this to increase the number of pieces of bread that can beContinue reading “Food and Scalars”
Numbers
While studying some of the higher content, a student made the comment, “Hey all they are doing is what we’re doing when we change from inches to centimeters.” Fancier words needed to keep definitions strict and clean can camouflage a basic idea.
Vectoreverything 