The continuum, Zeno's paradox and the price we pay for coordinates 117 | Math Foundations скачать в хорошем качестве

The continuum, Zeno's paradox and the price we pay for coordinates 117 | Math Foundations

In this video we venture into a range of topics, from the nature of the continuum, to the paradoxes of Zeno, to an understanding of some of the consequences for mathematics in the shift from geometry to arithmetic that flowed from the Cartesian revolution. As we let go of the real numbers, we must prepare ourselves to appreciate that the arithmetical view of geometry does not always exactly fit with our physical intuition. Our biology constrains us in important ways, and so guides our thinking down certain paths, for better or worse. If we demand that mathematics adheres to our biological orientation and physical intuitions, then we can be led astray. Such is the reason why modern pure mathematics has lost its way logically, with its unreasonable insistence that there is a theory of real numbers. Video Contents: 00:00 Giving up the dream of "real numbers" 3:45 How to model the continuum 6:51 Another version of Zeno's paradox 8:52 Nature of the physical continuum 12:10 Mathematical continuum 14:46 Physical/practical intuitions 20:10 Identifying straight lines and circles 23:31 Identifying order relations 25:12 The price we pay for co-ordinates 28:21 Geometry created from Cartesian approach ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист