# Course 2 -- Week 1 -- Normalizing inputs

Hello, I have a question about the cost function of the unnormalized case in this video. Why the contour of the function is not consistent with the direction of the J function? Shouldn’t the contour be perpendicular to the J axis?

Thank you

It’s possible that I’m simply missing your point, but the contours are of the J surface meaning that they are “sections” of the surface defined by a constant J value, right? So why would you expect them to be perpendicular to the J axis? It all depends on the shape of the surface, which is the point here, right? The goal of normalization is to make the contours more symmetric.

Thank you for your reply. Because the contour shares the same J value, so I think each contour should be parallel to the x-y surface just like the normalization case. I just don’t understand why for the unnormalized case, the cost function is not in parallel to the x-y surface.

It should be. Can you provide a reference to where you think it isn’t parallel? Which lecture and time offset?

It is Course 2 – Week 1 – Setting up your optimization problem – Normalizing Inputs. Around 3:25 you can see the upper left 3D plot (unnormalized case). Thank you.

It’s not a big deal. Here’s the slide:

The two pictures on the bottom are just being a bit lazy. He is showing you a projection of those contours down onto the 2D plane defined by w and b. Each colored circle in the right lower picture (e.g.) is actually suspended above the plane at a different level (lower as you go towards the center). In other words, imagine that you’re looking straight down the J axis in those pictures. They just didn’t take the trouble to create a real 3D rendering of it.

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