{"id":28494741,"date":"2021-04-12T11:06:51","date_gmt":"2021-04-12T18:06:51","guid":{"rendered":"https:\/\/nav.al\/?p=28494741"},"modified":"2025-11-07T08:14:39","modified_gmt":"2025-11-07T16:14:39","slug":"substrate","status":"publish","type":"post","link":"https:\/\/nav.al\/substrate","title":{"rendered":"Every Theory Is Held Inside a Physical Substrate"},"content":{"rendered":"\n

Naval:<\/strong> There goes my solution for Zeno\u2019s paradox<\/a>, which says before you can get all the way somewhere, you have to get halfway there. And before you can get halfway there, you have to get a quarter of the way there, and therefore, you\u2019ll never get there.<\/p>\n\n\n\n

One way to get past that is to say even a series of infinite things can have a finite sum. You run the infinite series<\/a> and sum it, and we learn pretty early on that it converges. Another thought I had was that you have to cover a minimum distance, the Planck length<\/a>, and therefore you will get there. It\u2019s a finite series of steps. But you\u2019re saying we just don\u2019t know.<\/p>\n\n\n\n

Brett:<\/strong> If the laws of physics say that we can cover one meter in a certain time period, then that\u2019s exactly what we\u2019ll do. And our current understanding of the laws of physics says precisely that. So Zeno\u2019s paradox is resolved simply by saying that we can cover this space in this amount of time. It\u2019s silent on whether or not space is infinitely divisible. <\/p>\n\n\n\n

When someone asks, \u201cIs space infinitely divisible?\u201d Then I would say, \u201c<\/strong>Yes, it is.\u201d<\/strong> They might turn around and say, \u201c<\/strong>How do you know?\u201d<\/strong> And I would say, \u201c<\/strong>General relativity.\u201d<\/strong> How do I know that\u2019s true? Well, I don\u2019t know that it\u2019s true. However, it is the best explanation that we presently have of space-time. And then they might get into a discussion about, \u201c<\/strong>Well, if it\u2019s infinitely divisible, then you\u2019re presented with Zeno\u2019s paradox all over again.\u201d<\/strong> And I would say, \u201c<\/strong>No, you refute that by a simple experiment.\u201d<\/strong><\/p>\n\n\n\n

So we don\u2019t know how it is, but we can travel through all of these infinite points if, in fact, there are infinite points. Zeno\u2019s paradox is about the domain of pure mathematics. But we don\u2019t live in a world of pure mathematics; we live in a world of physics. And if physics says that we can transverse an infinite number of points in a finite amount of time, then that\u2019s what we\u2019ll do regardless of the mathematics.<\/p>\n\n\n\n

Naval:<\/strong> Every mathematical theory is held inside a physical substrate of a brain or a computer. You\u2019re always bound by the laws of physics, and these pure, abstract domains may have no mappings to reality.<\/p>\n","protected":false},"excerpt":{"rendered":"

There goes my solution for Zeno\u2019s paradox<\/a>, which says before you can get all the way somewhere, you have to get halfway there. And before you can get halfway there, you have to get a quarter of the way there, and therefore, you\u2019ll never get there.<\/p>\n

One way to get past that is to say even a series of infinite things can have a finite sum.<\/span> More <\/i><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[6,9],"tags":[85,50,49],"class_list":["post-28494741","post","type-post","status-publish","format-standard","hentry","category-podcast","category-science","tag-epistemology","tag-philosophy","tag-science"],"acf":[],"yoast_head":"\nEvery Theory Is Held Inside a Physical Substrate<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nav.al\/substrate\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Every Theory Is Held Inside a Physical Substrate\" \/>\n<meta property=\"og:description\" content=\"There goes my solution for Zeno\u2019s paradox, which says before you can get all the way somewhere, you have to get halfway there. 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