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...
They split quaternion multiplication into two distinct operations: In modern high-level physics (like General Relativity or
The (measuring how much vectors go in the same direction). The "Vector Wars" Classical Vector Algebra became the
The (measuring the area between them and their perpendicular direction). 3. The "Vector Wars"
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.
By the early 1900s, the battle was over. In 1901, , a student of Gibbs, published Vector Analysis . This was the first true textbook in the modern sense. It standardized the notation we use in every physics and engineering classroom today (