Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

Re:Wolfram Alpha Is Making It Extremely Easy for Students to... by xiaoma on Friday July 07, 2017 @12:33PM (#14719729)

> "I think that if you see a complex equation, you should be able to roughly imagine it in your head."

This breaks down in many cases. What if your equation involves complex numbers for each component? What if it's an eight dimensional space or perhaps a multi-hundred dimensional space for recommender system?

At some point, you have to be comfortable with more abstract representations.

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Re:Wolfram Alpha Is Making It Extremely Easy for Students to... by adamnemecek on Friday July 07, 2017 @12:44PM (#14719824)

I think of complex numbers as just points/vectors.

As for multidimensional spaces, you might not be able to visualize all the dimensions at once but by doing them three dimensions at a time, you can go Pretty far.

You should check that the abstract representations still make sense intuitively.

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