Eight Lessons on Infinity by Haim Shapira
Author:Haim Shapira
Language: eng
Format: epub
Publisher: Watkins Media
We subtract the first equation from the second, and get:
Hence,
½ S = 1 and S = 2.
In other words, it will take precisely two minutes to travel infinite half points to get from A to B.
Frankly, this solution is not so surprising. We began by assuming that it takes one minute to get from A to C, which is exactly half the distance, and therefore one cannot be surprised that the entire distance will take two minutes.
Zeno would most certainly have objected vociferously to this solution, because we assumed what needed to be proven. When we said, “If we assume that it takes a minute to get from A to C”, we assumed that motion is possible and that we can get from A to C. However, that assumption is what needs to be proven, and this leads to what is called a circular proof.
Zeno would have probably clarified his standing by saying something similar to this: “How and on what grounds do you assume that you can get from point A to point C? It is totally obvious to me that you are making a monumental error. It’s as clear as the sun on a summer day on a beautiful Greek island, that before arriving at point C from point A, one must travel half that distance and reach point X. He then must travel another half of the remaining distance to C to reach point Y, and so on and so forth. You certainly realize that it is impossible to pass infinite halfway points in finite time. Therefore it is impossible to get from point A to point C, which is in contradiction of what you just said. I trust that you understand that it is also impossible to get from A to X, because here, too one must pass half the distance, and blah, blah, blah. The truth is that it is impossible to get from any point to any other point. In other words, it is impossible to even begin any sort of motion whatsoever.”
It seems that Zeno has won the day. Doesn’t it?
What do you think?
Download
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.
Biomathematics | Differential Equations |
Game Theory | Graph Theory |
Linear Programming | Probability & Statistics |
Statistics | Stochastic Modeling |
Vector Analysis |
Modelling of Convective Heat and Mass Transfer in Rotating Flows by Igor V. Shevchuk(6213)
Weapons of Math Destruction by Cathy O'Neil(5800)
Factfulness: Ten Reasons We're Wrong About the World – and Why Things Are Better Than You Think by Hans Rosling(4470)
Descartes' Error by Antonio Damasio(3150)
A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra) by Barbara Oakley(3090)
Factfulness_Ten Reasons We're Wrong About the World_and Why Things Are Better Than You Think by Hans Rosling(3034)
TCP IP by Todd Lammle(2995)
Applied Predictive Modeling by Max Kuhn & Kjell Johnson(2885)
Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb(2844)
The Tyranny of Metrics by Jerry Z. Muller(2826)
The Book of Numbers by Peter Bentley(2755)
The Great Unknown by Marcus du Sautoy(2522)
Once Upon an Algorithm by Martin Erwig(2465)
Easy Algebra Step-by-Step by Sandra Luna McCune(2445)
Lady Luck by Kristen Ashley(2393)
Practical Guide To Principal Component Methods in R (Multivariate Analysis Book 2) by Alboukadel Kassambara(2368)
Police Exams Prep 2018-2019 by Kaplan Test Prep(2340)
All Things Reconsidered by Bill Thompson III(2248)
Linear Time-Invariant Systems, Behaviors and Modules by Ulrich Oberst & Martin Scheicher & Ingrid Scheicher(2219)
