A Marriage of Intellect and Intuition

From the Gill Tarot, the King of Swords; from The Circle, "Fertility:"

          I find Gill makes use of some thought-provoking symbols for her King of Swords. The lightning suggests he leaves his mind open to inspiration and new ideas. The feathers on his throne hint that he realizes knowledge can change over time; just as a bird molts each year, some ideas should be left behind. Yet even more interesting is the keyword Gill assigns him: intuition. Most folks would think it odd to assign such a word to this intellectual ruler. Yet as neuroscientists and psychologists begin to study intuition more in depth, they're finding it's not quite the 'woo-woo' topic as originally thought. Today cognitive scientists think of intuition as a set of non-conscious cognitive and affective (emotional) processes. Intuition is faster than rational thinking (which sounds good), but it's not infallible. Yet the good news is it can get better with practice. Intuition is associative; it involves the brain's ability to pick up on recurring patterns. The more we are exposed to an area of knowledge, the easier it becomes for our brains to pick up on patterns that are relevant.
          Fertility (from The Circle deck) could be defined as the ability to produce and support the growth and development of something. That little egg will never mature without support, just as any concept or potential solution must have effort behind it. The King would prod me to see if my idea was more than a fleeting thought. Can I describe it in detail? What factual knowledge backs it up? Have I applied it in the real world or only in my head? Intuition may have helped me conceive the idea, but I'm going to need logic to prove its worth.