jim_doki said:
I believe Sherlock Holmes (or someone like that) said it best, "From the astrologer we got the astronomer, from the alchemist we got the chemist. Magics of yesterday are the sciences of today." (paraphrased)
When I consider this, it seems quite incorrect. Ancient civilizations which anthropomorphized or romanticized the movement of celestial bodies had also been studying them. If anything, I'd say that astronomy and astrology in this case went hand-in-hand, or that astronomy predated astrology. Studying numerous astrological legends, one can easily make a connection between an astrological figure and its corresponding celestial body, where the astrological record would usually closely follow astronomical observation of said body.
Before alchemy there was chemistry. Chemistry can be observed in the human record as the first purification and casting of iron into steel; herbal medicine; extracting silicon from sand to produce glass or to use while smelting various tools, making them more flexible; early-day napalm (Greek fire); Chinese fireworks. Chemistry was a practical science before alchemy was really at its peak, as a legend in Medieval Europe claiming knowledge of how to convert base metals into gold, concoct a youth-drink or some magical cure.
No, it was alchemy that was inspired by chemistry, if you ask me.
I believe it to be a trend that humans would adopt practical, scientifically sound methods of technology first, and then philosophize or attempt to explain a phenomenon with stories or hypotheses, both ordinary and supernatural. It is only during the scientific movement that I ever learned that humans stopped running their mouths, spinning bullshit to explain everything around them. It is science to exclude the supernatural and claim that nothing is illogical or inexplicable.
About .9bar: .9999...-ad infinitum equals 1, but not if it does not equal to infinity.
That is, something infinitely close to one is by literal definition equal to one. Theoretically, nothing exists which is immeasurable. If anything is infinitely close to something, it is that thing. No one can pick a number between .9999...-ad infinitum and 1, because no one can measure, conceive, or imagine such a small number that is infinitely small, characterizing that difference between the aforementioned number forms.
They are practically and literally the same thing. It is not illogical to say that we can calculate the value of pi to whatever decimal place that is sufficient, but it seems we may never be able to calculate it to the infinite decimal place, though our methods and accuracy of measurement would improve on and on.
Science (and mathematics is a science) is about accuracy and precision, not about exactness.