Would You Float At The Core Of The Earth?

Thought experiment...if you built a bedroom sized room at the center of the Earth, and you are in that room, which way is down? Please explain to me why if you are surrounded by the same amount of mass in every direction, how does that NOT EQUAL NET ZERO? In other words, would that not be the exact same thing as weightlessness? So what would an illustration of the curvature of Space look like at the center of a massive body? Wouldn’t there be a vortex of some sort? It’s kind of important to me to understand where I’m going wrong?
A 'Blue Marble' image of the Earth taken from the VIIRS instrument aboard NASA's most recently launched Earth-observing satellite - Suomi NPP. This composite image uses a number of swaths of the Earth's surface taken on January 4, 2012. The NPP satellite was renamed 'Suomi NPP' on January 24, 2012 to honor the late Verner E. Suomi of the University of Wisconsin. Image Credit: NASA/NOAA/GSFC/Suomi NPP/VIIRS/Norman Kuring

A 'Blue Marble' image of the Earth taken from the VIIRS instrument aboard NASA's most recently launched Earth-observing satellite - Suomi NPP. This composite image uses a number of swaths of the Earth's surface taken on January 4, 2012. The NPP satellite was renamed 'Suomi NPP' on January 24, 2012 to honor the late Verner E. Suomi of the University of Wisconsin. Image Credit: NASA/NOAA/GSFC/Suomi NPP/VIIRS/Norman Kuring

You very nearly got there! Let’s run with your example of a small room at the center of the Earth, but for my sanity, I’m going to make your room a sphere instead of a square, because everything else involved in this example is going to be round...

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