Some Light Reading on Calculus

Hmmm.... well this certainly was a nice, cut-and-dry reading - very straightforward and pretty much entirely based in "exact" math and history. Makes it somewhat difficult to think of much to say ethically/philosophically on the general reading as a whole. Yet I find that I would agree with this reading's other poster (Jason's "The Rate of Right and Wrong") in that an ethical spin on this very long reading of hard facts and proofs would most likely be focused on uncertainty - which makes perfect sense that our discussion last time ended with its brief introduction.
On that note, I would like to point out a psycho-philosophical observation I've made through the years: that we, as humans, feel a very strong necessity to cling to concrete, certain facts. Stemming from a terror of the unknown, we find some absolute "truth" that we rigorously cling to and, upon it, construct our entire understanding of the world. Sometimes that comes in the form of religion, where those who base their knowledge from the Bible claim it as absolute fact and, as a logical result, must therefore take its words literally. Most others (especially in modern times) prefer to base their concrete "certainties" on math and science, generally assumed to be disciplines of certainty itself. So it makes perfect sense that most would be terrified to think of the possibility that their entire understanding (and their perspectives on everything they know) is built on something that isn't absolutely certain.
And yet, for someone such as myself [someone else may conclude otherwise] who analytically questions everything they "know", I find that the only thing we can ever know for absolute certain is that there is nothing that we know with absolute certainty. Our knowledge of science is just the current (albeit tested) theories of observable trends; history often dwindles down to the perspectival interpretation of whoever recorded it; and math, being the archaic human method of explaining patterns/relationships of reality, is only fact insomuch as the situation's parameters define it as such.

This last becomes the major issue we see in the reading where the objections of others to either Newton's or Leibniz' approach to calculus seemed (as I understood the reading) to be concerned mainly with issues such as the logic behind the applicability of the concept of ratios with infinitesimal denominators; in short, with limits.
Though perhaps more of a curiosity than a substantive addition to this post, I cannot help but comment on the inability of us/myself as an observer in trying to objectively understand the entire context of this situation - including the historical context of the society (whose influential perspectives caused both Newton and Leibniz to refrain from publishing their "radical" ideas) as well as the sensibility of the math itself.
Using myself as an example, I once was in absolute concert with the objections set forth in the reading. Yet now, (having taken and understood multiple courses that explore and define the many aspects of calculus) I have become so mentally well-versed in the concepts of limits and infinitesimals that my method of logic itself has conformed to these ideas; accordingly, it is incredibly hard now to understand where these logical objections in the reading are coming from, and a "how does this not make sense to you" kind of attitude sets in, and I find it difficult if not impossible to be able to dissect their objections and truly prove the certainty of my current understanding against their arguments. As a result, having been unable (at least in terms of the modern state of such developed knowledge) to analyze the situation objectively, I often end up concluding teleologically that the ends justify the means, and that so long as that method calculus keeps giving us the observably "correct" results, that's all the proof we need. Then again, I'm not a true mathematician.

One final side observation I wanted to comment on was the personalities of each of these two brilliant pioneers as well as that of other proclaimed "geniuses" of history. Course I can't say this for everyone who has ever made a significant contribution to math, science, etc., but is it not curious that the most brilliant minds tend to be socially... unfit? For Newton (and probably the majority of other "geniuses" - Einstein comes to mind) of course this is obvious in his eccentricities and nervous irritability, while Leibniz' apparently profound philosophy had to be kept a secret in order for him to remain popular. And I mean this is by no means a novel idea - perhaps even an intuitive one since the only way evolutionary advancements can be made is when one abnormal ("mutated") individual is lucky enough to surpass the status quo; not to mention the mentally conducive environment that social aloofness provides for learning.
Even so, I just find it interesting that very nearly all aspects of social development encourage conforming to the standard norms (and necessarily so, in many cases), while progress and advancement rather clearly favors a highlight of the individual.