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 east into the direction where north used to be.”

“Standing by to rotate coordinate system… Done!”

“Any changes?”

“Sir, they have new components, they’re heading 30 kilometers per hour South.”

“Good, we needed that change.”

“Sir, look what happened after we made the coordinate change! They’re heading south, and heading south means they’re heading straight toward us!”

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