Is the brain axial?

The hypothalamus is sometimes called "the brain of the brain". It is the hub for many automatic and homeostatic systems, including the circulatory system, metabolic processes, and sensory inputs.

Nope! The spinal cord connects the brain to the rest of the nervous system in the body, sending and receiving signals. It is a conduit, nothing more.

There are around 200,000,000 brain cells in your brain.

Usually rack one's brain. However, according to Oxford dictionary online, it's either: PHRASES rack (or wrack) one's brains make a great mental effort. - ORIGIN from Dutch rec, Low German rek...

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