![]() Question 2: is the above analysis correct in suggesting that Aristotle is theorising the possibility of a quanta of power? Question 1: am I correct in thinking that this is at least one origin of the infinitesimal calculus, in the same way one takes the integration of areas in taking the limit of inscribed polygons by Archimedes? That this analysis in the limit of the small (not the large) follows immediately that of power (force), and motion suggests that it was understood by Aristotle that just above the limit of the small, these concepts are related linearly - hence his introduction of ratios and this is the notion that is quantified much later by the infinitesimal calculus of Newton and Liebniz and like Newton, perhaps not at all coincidentally - it was discovered, after all by the analysis of motion. ![]() no, it may well be it will cause no alteration or increase at all. an object half the size in half the amount of time. does not make it inevitable that it will alter. causes such-and-such an amount of alteration. However, the fact that agent of alteration. That is why Zeno is wrong in arguing that the tiniest fragment of millet makes a sound there is no reason why the fragment should be able to move in any amount of time the air which the whole bushel moved as it fell.Īnd this analysis appears to be ratified by what he writes in the last passage of the book: He connects this to a paradox of Zeno that is little known - at least I haven't come across it before. He means there is a physical limit to how small a power there is, ontologically speaking, that can cause motion a quanta or atom of power. If, it did, one man could move a ship, since the power of the haulers and the distance which they all moved the ship together are divisible by the number of haulers. This sounds plausible given our own experience, but looking at the passage in question it appears, at least to me, that Aristotle is supposing something entirely else - and this from his analysis of the paradoxes of Zeno he writes in Physics VII.5:Īfter all, the fact that a given power as a whole has moved an object such-and-such a distance does not mean that half the power will move it any distance in any time. Very practically, pointed out that there was a threshold to get something moving when there is resistance to friction: 'one man cannot move a ship' as he put it. Happy math.According to an article by Rowan, Aristotle This post is the table of contents for the series. A Calculus Analogy: Integrals as Multiplication.Understanding the need for small numbers (in progress).Learning Calculus: Overcoming Our Artificial Need for Precision.The elegance of calculus can be appreciated progressively: we don’t need astrophysics to enjoy a starry night. Dabble, skim and ignore the examples if needed - focus on the insights. The goal is to be concise, informal, and fun. This is my intuition-laced hat in the ring. We shouldn’t be struggling with the true meaning of a subject centuries after its invention. We don’t need another course repeating the definitions that confused us the first time ( Here’s the definition of a limit, again!). It’s a lack of insights, not information, that makes calculus hard. They’re a gut check, not the focus (if you want practice problems, the book has plenty). ![]() My goal is intuition, so this works well.Īs I study the chapters, I’ll share the insights I find and the concepts I struggled with. It teaches calculus using its original approach (infinitesimals), not the modern limit-based curriculum. I’m reading Elementary Calculus: An Infinitesimal Approach. ![]() I need a refresher - in fact, I need the insights I want to share! These articles are for us both (it’s what I’d want to relearn the subject), and here’s my approach: I started writing in a vacuum, but realized I don’t remember calculus. I want a calculus series that lets calculus be calculus - wild, interesting, and fun. No, nyet, nein! I know what I need: intuition ( What does it really mean?) followed by examples to back it up. The happy smiles tour: oversimplifications without examples (Calculus helps scientists solve problems!).The anal-retentive, rigorous treatment: written by math robots, for math robots!.The “bag of formulas”: memorize ‘em and move on.I’ve struggled with how to write about calculus. Update: there is now a Calculus Course available ![]()
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