As I went through the readings I was both impressed at the incredible developments of the Arab Mathematicians when Europe was in a period of mathematical stagnation during the Medieval period and I found myself considering repeatedly just what factors need to be present in a society for these kind of mathematical advancements to be made.
For instance, it's clear that a society that was only focused on the hereafter and spiritual understanding of a God stifled mathematical growth, but at the same time so to did a society focused solely on practicality like the Romans. I was particularly surprised that the Romans made no development in Mathematics (their running water and complex engineering would seem to counteract that to my mind), certainly they had the money and the leisure at hand to think about such things. So mathematical development is seems not to be solely a function of time and wealth, or even practicality.
The common aspects I see between between the Greek, Islamic, and Renaissance societies is that they 1)all encouraged curiosity, and for the Islamic and Renaissance societies 2) they had a tradition to build upon and 3) had centers of learning. Islamic societies were curious about the world around them because it was a method by which to learn about God, and they also had Madrasas--schools where one could learn and discuss--and a growing collection of Greek philosophical and mathematical literature gained through conquest by the growing Arab empires. Both Nobility and the Merchant class was willing to patron mathematics, giving scholars the ability to develop theories.
Similarly Renaissance thinkers had a theology that now taught them that to learn about nature and the world God had created was to learn about God, intellectualism was no longer sinful. A influx of greek(preserved by the arabs) and arab literature translated into latin gave the Renaissance men a tradition to grow upon. Finally there were colleges established to both teach and share these new traditions.
These are all aspects that I feel intuitively I knew, but I would have also thought that things like practicality and need, would drive invention. Furthermore, could a society have just a one or two of the qualities a I describe and still have mathematical developments like we see in the Islamic and Renaissance societies?
For instance, it's clear that a society that was only focused on the hereafter and spiritual understanding of a God stifled mathematical growth, but at the same time so to did a society focused solely on practicality like the Romans. I was particularly surprised that the Romans made no development in Mathematics (their running water and complex engineering would seem to counteract that to my mind), certainly they had the money and the leisure at hand to think about such things. So mathematical development is seems not to be solely a function of time and wealth, or even practicality.
The common aspects I see between between the Greek, Islamic, and Renaissance societies is that they 1)all encouraged curiosity, and for the Islamic and Renaissance societies 2) they had a tradition to build upon and 3) had centers of learning. Islamic societies were curious about the world around them because it was a method by which to learn about God, and they also had Madrasas--schools where one could learn and discuss--and a growing collection of Greek philosophical and mathematical literature gained through conquest by the growing Arab empires. Both Nobility and the Merchant class was willing to patron mathematics, giving scholars the ability to develop theories.
Similarly Renaissance thinkers had a theology that now taught them that to learn about nature and the world God had created was to learn about God, intellectualism was no longer sinful. A influx of greek(preserved by the arabs) and arab literature translated into latin gave the Renaissance men a tradition to grow upon. Finally there were colleges established to both teach and share these new traditions.
These are all aspects that I feel intuitively I knew, but I would have also thought that things like practicality and need, would drive invention. Furthermore, could a society have just a one or two of the qualities a I describe and still have mathematical developments like we see in the Islamic and Renaissance societies?
In agreement with Sophie's response I'd like to add that it seems like the Arab train of scientific thought started to look into mathematics for speculation's sake as well as practicality. They used each other previous findings to try and create a more controllable world but at the same time tried to push mathematics further along for the sake of scientific thought. The translation of ancient texts they translated from Greek and Latin would give testament to their value of mathematics both in the practical and historical sense.
ReplyDeleteI agree that there seems to be more to advancing mathematical thought then just leisurely time and practicality but I also feel that one more missing factor, in addition to curiosity, tradition, and learning centers is valuing scientific thought in a speculative sense and overcoming the practicality barrier.
I think that last point you made really hit home. Speculatively valuing scientific thought regardless of practicality; science for the sake of science; a love of science, if you will - or, more particularly, a love of knowledge.
DeleteI mean we can extrapolate from everyday experience that it's not enough to just have a lot of leisure time - I mean how much of today's leisure is "wasted" on the internet? And even discovery for practicality has its limits, because once a more efficient method has been found to work, why bother yourself with more theory? If necessary, a common (though perhaps extreme) example of this everyone who is too lazy to get off the couch and change the channel on the TV. Thus, the remote was invented, and now that it is and it works, why spend energy trying to improve it?
Indeed I think that perhaps the most important factor is the love and desire for knowledge and understanding of the world around us, even if it has absolutely no current practical use.
But how does such a factor come about? I think we do know that it is/can be directly correlated with religion provided that the subjects, like the Muslims and the Renaissance Christians, are able to mentally unify the desire for both spiritual and scientific knowledge.
But which begets/inspires the other? I'd like to think that, as society evolves, so too does wisdom, but that is hardly the case. I mean look at the whole "age-old" science vs. religion debate [anyone seen Angels and Demons?]. There are all too many people today that think the Church (or any other religion) wars with or is in any way against scientific discovery, when in reality we see from this very article that the two are - and should be - two sides of the same pursuit of knowledge. Granted, there does appear to be an increasing proclivity of people in the world today who, regardless of their religion or lack thereof, seem to relish the pursuit of knowledge of all forms. But just think of how long it took to reach this point - it was at least 700 years after individuals starting openly unifying knowledge that the majority of the rest of the populace started to follow suit.
Thus, in answer to the question of what inspires the love of knowledge/science for the sake of science regardless of practicality, I feel I must simply turn to the individual. I think that there are certain hereditary affinities of one's personality (which, being passed down generations, do indeed evolve convergently with time) that, when exposed to a certain environment that actively displays the value of knowledge and cultivates the pursuit of speculative knowledge in spite of practicality, I think that those are the two factors that contribute to a love of science/knowledge and in turn provide the greatest contribution to scientific discovery.
In response to both Sophie and Jamison, the mathematical push to make sense of religion and faith fascinates me. Math requires a set of patterns, set parameters, algorithmic inputs and outputs. But faith often evokes a sense of the unknown, of stepping out on the edge with no statistical way to predict what is going to happen other than mathematically unfounded beliefs.
ReplyDeleteYet as pointed out by the articles, math and religion can be codependent. Monks needed math to keep the time while, as Jamison pointed out, a speculative drive to overcome "the practicality barrier" of math evokes a faith to step into the unknown hoping to find answers. Thomas Aquinas' Summa Theologiae is another example pointed out by the readings of a synthesis between the seemingly different fields of scientific reason and faith.
With this said, the marriage between math and religion seems unavoidable. As a parting thought on this, if scientists could show that electromagnetism and the weak nuclear force are "manifestations of a single force," one day will we prove that all forces of nature (i.e. the strong force, gravity and electromagnetism) are manifestations of one single force, and is this proof of a Supreme Being, a Divine Instigator? Or just cleaner math? Some may argue both.
Jason, I think that your questions about the interpretation of the unification of the fundamental forces of nature is an interesting one that I had not considered before. That being said, I think that the motivating purpose for unifying the forces is more of an aesthetic/philosophical motivation rather than a necessarily practical one. Although, that is not to say there isn't hard evidence that shows that some of the forces are equivalent during certain epochs of the early universe, but their unification is only relevant in those physical regiems (namely very hot, dense states of matter that would be equivalent to the early universe in big bang cosmology).
DeleteI did find that in these readings, while religious motivations did exist for advancing some aspects of human understanding of the universe and mathematics, there was also an inhibition for advancements that seemed to contradict religion-based cosmological views. In particular, certain astronomical theories were championed, not because observation matched the theory, but rather because the spiritual interpretation of it was pleasing. Notably, Ptolmey's celestial spheres placed the earth at the center of the universe and everything else had "perfect" circular orbits around the earth. This, however, could be farther from the truth, and indeed the ancients were aware of this as arabic astronomers like Al-Tusi had to fiat in so-called epicycles into certain planet orbits in order for the theory to match observation. Most likely, they were accounting for retrograde motion (where a planet appears to reverse its orbital direction for a period of time as the earth's vantage point shifts).