A colleague alerted me to a recent published book entitled, Is Science Western in Origin? by Indian physicist, C.K. Raju. Not too surprisingly, he discovers otherwise (says the back cover)

On stock Western history, science originated among the Greeks, and then developed in post-renaissance Europe. This story was fabricated in three phases.
 * First, during the Crusades, scientific knowledge from across the world, in captured Arabic books, was given a theologically-correct origin by claiming it was all transmitted from the Greeks. The key cases of Euclid (geometry) and Claudius Ptolemy (astronomy)—both concocted figures—are used to illustrate this process.
 * Second, during the Inquisition, world scientific knowledge was again assigned a theologically-correct origin by claiming it was *not* transmitted from others, but was “independently rediscovered” by Europeans. The cases of Copernicus and Newton (calculus) illustrate this process of “revolution by rediscovery”.
 * Third, the appropriated knowledge was reinterpreted and aligned to post-Crusade theology. Colonial and racist historians exploited this, arguing that the (theologically) “correct” version of scientific knowledge (geometry, calculus, etc.) existed only in Europe. 
These processes of appropriation continue to this day.

Is it true that the West merely appropriated science from other cultures and "laundered" it to make it look Greek? Did the West steal everything that made it powerful? Did the West borrow Science or invent it?

There is more than bragging rights going on in this debate, for various groups have appropriated the rise of Science as proof of their sweeping claims. For example, John William Draper's 1874 "History of the Conflict between Religion and Science" and Andrew Dickson White's 1896 "A History of the Warfare of Science with Theology in Christendom" coupled the rise of Science with growing atheist sentiment. Or during the 1920's the rise of Science was used to support a racist superiority of northern Europeans over southern, or Europe over Asia. More recently, the UN's IPCC has used the science of climate change as justification for a sweeping global power grab. So what is responsible for the rise of science and the transfer of power--luck or prowess?

This is the sort of question we used to ask 20 years ago, when Japan had all the innovative electronics, but the US had all the patents. Was there something about the US that made innovation possible but stifled implementation, or were US scientists just more creative but gullible? In a similar vein, was the success of Science in the West fundamentally a strategic, internal, and theoretical advantage (better genes, better religion), or merely a tactical, external, and practical advantage (higher income, longer life)?

Grouping the (non-exhaustive) responses into these two categories, we find the following answers:

Strategic:
  Genius theory: The West had more genii such as Newton, Huygens, Leibniz, Faraday, Maxwell, Heisenberg, Gödel, and Einstein.
  Christianity theory: The West had a superior metaphysical understanding of science.
  Racist theory: The West had better genes, more genii, etc.

Tactical:
  Stolen theory: The West were better copycats. (See above reference to Japanese electronics)
  Capitalism theory: The West had more leisure time because of superior economic environment.
  Health-care theory: The West had higher productivity because their wise had better health care. (Obama take note!)
   Accident theory: The West just had an improbable collection of lucky events.

Robert K. Merton, a sociologist at Columbia University (and thus by definition an anti-metaphysical advocate of naturalism), argued that it was external, practical factors that caused the West to succeed in his 1938 article, Science, Technology & Society in Seventeenth-Century England, principally the Protestant ethic (shades of Max Weber) that also inspired Capitalism. You might also compare this sort of analysis with that of Jared Diamond, whose 2005 "Guns, Germs and Steel" argued the same sort of external factors for the success of Western technology.

In contrast, Rodney Stark, a historian at Baylor University used the database of Chinese, Greek, Arabian and European science to argue that it was an internal, philosophical difference. The conclusion of his 2005 book, The Victory of Reason, was that Christianity provided the theoretical foundation that led to all the other practical benefits. The real credit for his thesis probably belongs to the late physicist-philosopher, Stanley Jaki, who argued in his 1990 Science and Creation, that it was the superior metaphysics of Christianity that could take Science out of the superstition that waylaid other cultures. (Jaki also credits Pierre Duhem and Alfred North Whitehead, who along with Nicolai Berdyaev, M. B. Foster, and R. G. Collingwood formulated this thesis decades earlier in opposition to the Merton theory.) This thesis was developed by Michael Bumbulis in a 1996 whitepaper. Eric Snow does a nice job summarizing the arguments in his 1997 review.

Then there are those who thread a course between the Merton accident and the Duhem miracle. John Mark Reynolds in his 2009 "When Athens Met Jerusalem" holds that it was the collision between Greek pagan thought and Christian elevated metaphysics that provided the explosive power of the Renaissance. Of course one should give the ancients their due, but which ones? C.K. Raju would argue that it was really Indian physics that collided with Christianity, and then the debate settles into a Merton/Diamond sort of conglomerate about all the accidents of history. So despite Reynolds attempt to diminish Christian arrogance or elevate Greek classicists, he cannot hold a middle ground. Either the miracle of Christian philosophy was the magic ingredient, or it was an accident of circumstance, which is to say, the conclusion is forgone in the assumptions.

Well as you might guess, Stark's conclusion nettles those who prefer a Draper-White conclusion, or a Raju sour-grapes response. One academic, Richard Carrier, prefers to take his objections on the road (rather than, say, an obscure academic journal). Here's his blog/YouTube dissent, pointing out that Stark has made some historical blunders in his book. (Though it would seem that Carrier's strawman arguments don't address the underlying work of Duhem-Jaki-Bumbulis-Snow.)

In addition to all these carefully reasoned arguments by Snow and Stark, I've been more and more convinced that it was not metaphysics per se, but theology that made the difference. That is, metaphysics is not an acquired taste, but an indoctrinated one. And the principal means of indoctrination is religious instruction. Thus it is not the metaphysics of Christianity that makes Christians different, but the theological content, the creeds, the confessions that make it unique. The metaphysics is, as it were, merely the intellectual dressing on the naked body of belief.

And what is that belief that led to the emergence of Science? The Trinity.

For the scylla and charybdis of science are transcendent monotheism and immanent polytheism. The first allows no rational causes to hold, the second holds to no rational effects. The intermediate belief of science as both permanent and peculiar, both global and local, is a tenuous and impossible place to stand unless there be a third thing, a tertium quid of equal immanence/transcendence, global/local, permanent/peculiar, which is only provided by Christianity.

The problem is what to do with Reason.

Let me simplify by lumping animism, Greek polytheism, and Zoroastrian dualism into the same bin as Hindu pantheism. They are all alike in having an immanent god(s), an absolute which is part of the same world that you and I inhabit. This god can be touched, can be changed, can be affected by our entreaties. It is not that this god is sometimes approachable, but that he cannot avoid being approachable. For him, the hard part is staying godlike and not devolving into sub-godlike behavior.

Okay, now what do we do with Reason? Is it approachable? Is it changeable? Can it respond to entreaties? Is it made from the same stuff as us? If this seems too abstract to follow, imagine Reason is a Math Theorem. Does a math theorem respond to special pleading?

Thus an immanent god might be rational one day, and irrational the next. Or even if he were rational 99% of the time, the one time you need absolute and total assurance, he would let you down.

Pantheism/polytheism cannot handle absolutes, and therefore cannot formulate laws.

Post hoc interpretations of history showing science to emerge from Christianity, while true, aren't really enough. At the very least, from a rhetorical perspective, it looks more like a turf battle. What would really decide the debate is not only saying "Christianity best explains science" but going further and saying "Christianity not only explains science, but qualitatively improves upon our modern idea of science in a way inseparable from Christianity."

This is because you want a "scientific explanation" for the evolution of science! If you were a Muslim, post hoc is more than sufficient explanation--Allah wills it so. And if you were a Hindu, then post hoc is the mind of maker. It is only that you are neither, but rather a scientist, that you want a positive metaphysical explanation for the origin of science. The difficulty is that the very desire is a consequence of Christianity, so in order to explain the spiritual roots of the fulfillment, it is necessary to explain the spiritual roots of the desire. But should the desire be denied, then so also the fulfillment.

So, to move the debate in that direction, here's my question: Given that Christianity provides grounds for expecting the world to be rationally formed, why should we then expect it to be humanly understandable?

You began by rejecting the polytheistic position, and positing Reason. Having made your foundation in the transcendent absolute of Reason, you then wonder how it can be immanent. How can it be that this cold and rational god of Math who lives in a Hilbert space of infinite dimensionality could stoop down to make sense in my finite 3-dimensional existence? This is the opposite problem confronted by Islam, that God, who is absolute, is not forced to "make sense" to me. Rationality is, after all, merely the projection of infinite Reason into a my small finite brain, and is therefore a subset of all that God is. All squares are rectangles, and all rectangles are parallel quadrilaterals, but not all parallel quadrilaterals are squares. To my square mind it might be impossible to explain rectangles not to mention the parallelograms of God.

Thus comes the need for the intermediate mediator, the immanent transcendence, the absolute peculiar, the global locality, the transfinite 3D set, the god-man bridge. But this third thing cannot be a mixture, it cannot be even a compound, it must be indivisibly both, a tertium quid. And that means the metaphysical world cannot be a one-dimensional polarity, a single axis between two extremes, but it has to have a second axis with a third point. There must be a metaphysical trinity for such an absolute not to collapse into one or the other extremes. This was the message I learned from Vladimir Lossky's book "In the Image and Likeness of God" where he spends considerable effort on the necessity of metaphysical trinities.

Only Christianity posited such a thing. Only Christianity permitted Science.

Plus, it is not only Christianity that posited a rationally created world. So did Plato and Virgil. What exactly is unique in Christianity's contribution? I suspect the first question may provide an answer to the second, but that's just a guess at this point.

One can stand at either end of a single-axis world and pine for the riches of the other. Plato's absolutes desired immanence, but all he could offer were the shadows on the cave wall. The Hindu promised the nirvana of the absolute, but could only offer the wheel of reincarnation, endlessly turning without arriving. For pining is not possessing.

Neither of these could offer what Christianity had, and that was the very real substance of the absolute God, the very real access of human mercy to the terrifying transcendence of absolute justice. Only Christianity had a Christ who was neither swallowed up in Reason nor subjected to human decay. This tension is what makes Science possible, and without it, Science rapidly turns into one or the other.

For illustration, global warming is a scientific theory that has taken on moral aspects. Read that interview with the Greenpeace president, watch Gore's movie, the truth is less important than the moral imperative of global warming. This is what happens when science drifts toward transcendence, it becomes dogmatic.

The opposite extreme is when science attempts to be practical, to be immanent without understanding the metaphysics. Denyse O'Leary's The Spiritual Brain shows how neuroscience attempts to draw conclusions without understanding the mind. The field becomes rife with recipes, or comical "just so" stories to replace the metaphysics. In the end, one makes up stories "what ain't so" to formulate a quasi-metaphysical explanation for behavior one wanted to rationalize in the first place.

Neither global warming nor evolutionary psychology are Science, but for opposite reasons; the first abuses reason for the sake of morality, the second for immorality. But I stress that this story of two sciences is not unique to the 21st century, but is precisely the sort of barrier Jaki identifies when he said that Chinese, Greek, and Arabic science were not able to make progress. They were not Trinitarian.

So to answer CK Raju's question, Science is as western as Trinitarian theology is western. And no, trinitarian theology was not appropriated,  it was revealed.