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Swords are forged in fire, so the fire reading makes the cards a bit more physical and constructive than with air. Yet, a swordsmith is a rare and unique profession today, so they require no less deep strategy, study, experience, logic and intellect than if they were still air symbols.
The most expressive natural aspect of airy wands are trees. Swaying trees are a visible sign of the presence of air, and they continually grow upward and outward. Trees are sources of air for us. Wands also function as hollow tubes to channel and focus air, as musical instruments, smoking items, etc. Arrows, spears, and long projectile weapons are arguably even more representative of air than fire, such as 8 of Wands.
The Kundalini serpent and human spine are often used as example of spiritual energy flowing and circling up and down into the body and out of it. Wands focus and control air in ways that swords don't.