You are right it has both solid and liquid properties. It truly is a ‘paste’, also known as a ‘Bingham Plastic’. That is a material that sits still without flowing when stationary on your toothbrush (it doesn’t even slowly run off the side over time) but given enough of a squeeze does begin to flow like a liquid.
There are other weird materials out there. Have a look for ‘Non-Newtonian’ fluids. These do the opposite thing: when you give them a squeeze they become more solid! If you mix it right, you could walk over a swimming pool of custard because it turns solid when you step on it but liquid if you stand still!
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