The (measuring how much vectors go in the same direction).
In modern high-level physics (like General Relativity or Quantum Mechanics), we’ve actually circled back to more complex structures like Tensors and Spinors that look a lot more like those "monstrous" quaternions than Hamilton ever could have dreamed.
By the late 19th century, scientists were frustrated. had written his famous equations for electromagnetism using quaternions, but they were so dense that almost no one could solve them. Classical Vector Algebra (Textbooks in Mathemat...
Hamilton believed quaternions were the ultimate language of the universe. However, they were incredibly difficult to use. To do simple physics, you had to drag around a complicated four-part number when you really only cared about three-dimensional space. 2. The Great Schism (1880s)
The traditionalists were furious. , Hamilton’s successor, called Gibbs’s new algebra a "hermaphrodite monster." He believed that by removing the "quaternion" structure, Gibbs and Heaviside were destroying the mathematical soul of physics. The (measuring how much vectors go in the same direction)
Classical Vector Algebra became the "gold standard" because it was practical. It allowed us to build bridges, fly planes, and understand electricity without the overhead of 4D hyper-complex numbers.
They split quaternion multiplication into two distinct operations: had written his famous equations for electromagnetism using
But Heaviside didn't care about "mathematical elegance." He was a telegraph engineer who wanted tools that worked. He famously said, "Vectors are a great help to a man who has any physics in him." He used this "new" vector algebra to condense Maxwell’s 20 original equations down to the 4 we use today. 4. Victory and the Modern Textbook