I cannot imagine why this is a question. There is no physical evidence of three spatial dimensions - no matter how many rulers and clocks you choose to hold in my face as evidence. That would be mistaking your behavior for a physical reality. On the other hand, actions do have dimensions, so there is nothing lost in spite of the criticism.
Update: In terms of the dimension defined by xhiS (in a later post), it is meaningful to ask about things like the dimension of the space around an atom, without having a built-in 3D assumption.
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