Mind Matters Natural and Artificial Intelligence News and Analysis

# TagAlgebra

## The Vector Algebra Wars: A Word in Defense of Clifford Algebra

A well-recognized, deep problem with using complex numbers as vectors is that they only really work with two dimensions

Vector algebra is the manipulation of directional quantities. Vector algebra is extremely important in physics because so many of the quantities involved are directional. If two cars hit each other at an angle, the resulting direction of the cars is based not only on the speed they were traveling, but also on the specific angle they were moving at. Even if you’ve never formally taken a course in vector algebra, you probably have some experience with the easiest form of vector algebra — complex numbers (i.e., numbers that include the imaginary number i). In a complex number, you no longer have a number line, but, instead, you have a number plane. The image below shows the relationship between the real Read More ›

## Further Dispatches From the War on Math

Discussions of social policy where math is relevant can be useful. But a student who does not understand how an equation works will fail at both math AND social policy

Earlier this year, I reposted an article that originally ran at Salvo on the war on the teaching of mathematics as a discipline in publicly funded schools in North America. The war continues so here are some updates: Recently, three mathematicians who immigrated to the United States weighed in: The United States has been dominant in the mathematical sciences since the mass exodus of European scientists in the 1930s. Because mathematics is the basis of science—as well as virtually all major technological advances, including scientific computing, climate modelling, artificial intelligence, cybersecurity, and robotics—US leadership in math has supplied our country with an enormous strategic advantage. But for various reasons, three of which we set out below, the United States is Read More ›

## The Needless Complexity of Modern Calculus

How 18th century mathematicians complicated calculus to avoid the criticisms of a bishop
Would you be surprised if I told you that the essentials of calculus are actually very straightforward and simple? Read More ›

## Yes, There Really Is a War on Math in Our Schools

Pundits differ as to the causes but here are some facts parents should know

The Oregon Department of Education (ODE) recently encouraged teachers to register for training that encourages “ethnomathematics,” an education trend that argues, “among other things, that White supremacy manifests itself in the focus on finding the right answer”: “The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so,” the document for the “Equitable Math” toolkit reads. “Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict.” … An associated “Dismantling Racism” workbook, linked within the toolkit, similarly identifies “objectivity” — described as “the belief that there is such a thing as being objective or ‘neutral’” — as a characteristic of White supremacy. Instead Read More ›