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Linear regression is ML. You are off base.

That's cool. Can you explain what machines they were using in the 1800s to do learning on?

Does this mean if I simulate a neural network on pen and paper that stops being machine learning?

All of these are machine learning techniques. Doing it by hand doesn't change anything. Today we use machines so it's machine learning

I've worked out a 3x3 neural network with two pieces of labeled data by hand. Give me my statistics degree!

You're using the word to define the concept rather than the concept to define the word. Wrong order.

See: "Program".