Why is it that science arose in very few cultures and only persisted to turn into a rigourous self correcting discipline in judeo christian societies?
There are some basic philosophical aspects to Christianity that encourage science, while the different views in other cultures discourage science. For starters, if God created the universe, then it is real and subject to ultimate truth, not merely an illusion of the senses as some philosophies see it. There is little point studying something that doesn't exist. If a single god created the universe and that god is rational and caring, then the universe he has created would be rational and consistent. If it weren't then natural philosophy (ie science) would just be about recording a series of random events that have no predictive value. Furthermore the natural world (including humans) consist of things created by god, rather than gods themselves. Thus there is nothing to fear in what may be discovered, no taboos in knowledge, and seeking to understand the world is seeking to understand God's creation. Cutting up a frog is not cutting up a god. Most of the famous scientists whose equations and constants we use in physics and chemistry were devout Christians, and sought to know God through his works. The Bible describes God's creation as being both real, and good - therefor worth studying. The idea of consistent 'natural laws' were first derived from the Bible rather than from nature and nature was studied with the expectation of finding natural laws. Finally, man was created in the image of God, so you would expect us to be able to understand God's creation - perhaps this is why maths (an entirely human construction) is so powerful in describing the natural world.
It is only a very recent change that has seen science portrayed as an enemy of Christianity, apparently by people who sought to use this to discredit Christianity.