Curiosity is one of God's greatest attributes and one of humanity's coolest characteristics.

Love is the power to burst out of limitations and experience unity with other forms.  Curiosity is a form of this power.  It is the impulse, expressed through the intellect, to imagine the truth of something other than self.  Curiosity is a compound of consciousness formed by imagination and longing.  If God created the universe as a mechanism to explore His own infinite nature, curiosity must inevitably permeate creation as an experiment of consciousness, as a shadow of God's wish to know Himself.

Curiosity is latent in every evolving form on this planet, even before consciousness reaches full maturity in the human form.  I am not aware of say, a grub displaying much curiosity, but anybody with a dog has amusing anecdotes of curiosity in an animal.  The acceleration of curiosity in primates is a major contributor to the momentum powering the leviathan leap in intellect in human beings.  Charles Darwin observed the phenomenon of curiosity in animals, especially in primates:

From Descent of Man by Charles Darwin, Chapter 3

All animals feel Wonder, and many exhibit Curiosity. They sometimes suffer from this latter quality, as when the hunter plays antics and thus attracts them; I have witnessed this with deer, and so it is with the wary chamois, and with some kinds of wild-ducks. Brehm gives a curious account of the instinctive dread, which his monkeys exhibited, for snakes; but their curiosity was so great that they could not desist from occasionally satiating their horror in a most human fashion, by lifting up the lid of the box in which the snakes were kept. I was so much surprised at this account, that I took a stuffed and coiled-up snake into the monkey-house at the Zoological Gardens, and the excitement thus caused was one of the most curious spectacles which I ever beheld. Three species of Cercopithecus were the most alarmed; they dashed about their cages, and uttered sharp signal cries of danger, which were understood by the other monkeys. A few young monkeys and one old Anubis baboon alone took no notice of the snake. I then placed the stuffed specimen on the ground in one of the larger compartments. After a time all the monkeys collected round it in a large circle, and staring intently, presented a most ludicrous appearance. They became extremely nervous; so that when a wooden ball, with which they were familiar as a plaything, was accidentally moved in the straw, under which it was partly hidden, they all instantly started away. These monkeys behaved very differently when a dead fish, a mouse, a living turtle, and other new objects were placed in their cages; for though at first frightened, they soon approached, handled and examined them. I then placed a live snake in a paper bag, with the mouth loosely closed, in one of the larger compartments. One of the monkeys immediately approached, cautiously opened the bag a little, peeped in, and instantly dashed away. Then I witnessed what Brehm has described, for monkey after monkey, with head raised high and turned on one side, could not resist taking a momentary peep into the upright bag, at the dreadful object lying quietly at the bottom.

Apes look timorously into bags; humans invent herpetology.

If the fuel of creativity is inspiration, the invisible engine of creativity is curiosity.  Curiosity is in essence a spiritual engine.  Science accumulates facts and information using intellect.  But does science, especially paradigm-changing science, arise solely from intellectual machinations?  Was the driving force behind Darwin's inspiration qualitatively different from what compelled Milton to put words on paper?  When Einstein published his three radical papers in 1905, did those surprising notions not arise from curiosity?

What is scientific or artistic surprise but a moment in which God's timeless wish to know Himself, expressed through curiosity, becomes vividly conscious in the individual mind?  Art and science languish without inspiration, which is asleep without curiosity.  Surprise is an excellent consequence of curiosity, a delightful shadow cast by the transitory culmination of the fundamental impulse of curiosity.  A surprising way of looking at nature can happen after laborious reasoning, or it can happen like a sudden breeze on a still day; it can happen in a laboratory or in a dream.  Perhaps one way of judging a work of art or great advancement in science is the potency of the surprise one feels even after it has become familiar.

Curiosity is universal, infinitely miscible in the fabric of creation, and therefore infinitely free.  But it is also an experience of individual consciousness.  That is why societies that value the freedom of the individual tend to produce the greatest contributions to mankind's development.

Undoubtedly, the future will bring artistic forms as far removed from today's art as Photoshop is from prehistoric cave painting, and will bring scientific insights as far removed from primordial fascination with fire is from our ability to split atoms for electrical power.  But whatever artistic and scientific wonders the future holds, they will all be products of curiosity.

Keeping in mind that everything in our understanding of creation is an approximation, one way of understanding curiosity is as an approximation that can be expressed as a classical velocity of consciousness:

where C = curiosity,

L = longing, and

I = imagination.

Perhaps somebody else will be curious enough to look into this idea more rigorously.