tag:blogger.com,1999:blog-7739403784714088758.post6522094739813691668..comments2020-07-03T04:19:51.056-07:00Comments on The Philosopher: Zeno and the Demonstration of Infinity (2018)docmartincohenhttp://www.blogger.com/profile/07116346310852077070noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-7739403784714088758.post-1718666894605346312019-02-28T08:19:13.260-08:002019-02-28T08:19:13.260-08:00Thank you, Hugo, for your interesting and informat...Thank you, Hugo, for your interesting and informative discussion of a complex topic.<br /><br />My struggle is even envisioning what spatial, temporal, or numerical infinities actually are, in terms that are concrete, not ethereally abstract. I suspect I’m not alone. Definitions of infinity often strike me as circular and tautological. Expressions like ‘no beyondness’ generally complicate, not explicate. As do commonplace terms, I believe, like ‘boundless’, ‘immeasurable’, ‘endless’, and ‘uncountable’. For me, putative infinities, qualified infinities, infinities based in paradoxes, infinities based in thought experiments, and all other varieties of infinities seem unsatisfyingly manufactured rather than incontrovertible. (Though good grist for poets and artists.)<br /><br />In many cases, I’m hard put to think of stuff, conditions, relations, and events being infinite without their having been refuted by someone in some fashion at some time: infinite multiverses, the density at the center of a black hole, Cantor’s infinite set of numbers, the arrow of time and of entropy, Zeno’s infinitely divisible line, Hilbert’s infinite hotel paradox. And so on (whew, I almost slipped and said ‘ad infinitum’). Few, if any, of these examples are categorical. Not all, if any, help us get to that feel-good eureka moment of indubitably comprehending the concept. At various times and with different degrees of success, most (all?) supposed infinities have fallen under the raised-eyebrow scrutiny of philosophers, scientists, and mathematicians. Frankly, I’m not sure to what measure.<br /><br />As an indulgence in a hypothetical, let’s assume ‘infinity’ happens to have the feature of looking backward as well as forward. (Contrary to the ‘finite past–infinite future’ model.) That is, our being able to temporally and spatially leap back before the Big Bang — if ‘before the Big Bang’ even makes sense. I wonder if the result of that backward-looking feature would ultimately lead to ‘nothingness’ — to be clear, not entailing properties like quantum fluctuations flitting in and out, but categorical nothingness littered with its own assortment of snags. Two conundrums for the price of one: infinity and nothingness.<br /><br />All rather head-scratching, I find. But thank you, Hugo, for putting the topic center stage, for us to think about further.<br />Keithhttps://www.blogger.com/profile/05120485893579137602noreply@blogger.com