{"id":25368,"date":"2021-03-10T00:00:03","date_gmt":"2021-03-10T00:00:03","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=25368"},"modified":"2024-05-21T09:45:05","modified_gmt":"2024-05-21T09:45:05","slug":"deterministic-and-indeterministic-processes","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/en\/deterministic-and-indeterministic-processes\/","title":{"rendered":"Deterministic and Indeterministic Processes"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Deterministic and Indeterministic Processes, Probabilities and Chance<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>Summary<\/strong><br \/><em>In this introductory class to Probability Theory, we will explore the connection between deterministic and indeterministic processes and their relationship with probabilities and chance. We will see how processes in nature are classified into two mutually exclusive species and how they are understood through deterministic and indeterministic models. In addition, we will examine how the lack of control over the environment and initial conditions leads to indeterministic processes and the need to deal with a multitude of possible states. Finally, we will address the topic of chance and probabilities, analyzing the example of a coin toss and how the understanding of probability is obtained from experiments with equiprobable outcomes.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>LEARNING OBJECTIVES:<\/strong><br \/>\nUpon completing this class, the student will be able to:\n<\/p>\n<ol>\n<li><strong>Understand<\/strong> the nature of models and their relationship with deterministic and indeterministic processes.<\/li>\n<li><strong>Understand<\/strong> the relationship between chance and indeterministic processes.<\/li>\n<li><strong>Identify<\/strong> the necessary conditions for a process to be considered random.<\/li>\n<li><strong>Identify<\/strong> equiprobable outcomes and how they are used to understand probability.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>TABLE OF CONTENTS<\/strong><br \/>\n<a href=\"#1\">BASIC IDEAS<\/a><br \/>\n<a href=\"#1\">DETERMINISTIC AND INDETERMINISTIC PROCESSES IN NATURE<\/a><br \/>\n<a href=\"#1\">PROBABILITIES AND CHANCE<\/a><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/DsDU0MjD_XY\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Basic Ideas<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DsDU0MjD_XY&amp;t=123s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">To begin our study on Probability Theory,<\/span><\/strong><\/a> we must first explore the connection that exists between deterministic and indeterministic processes and their relationship with probabilities and chance. The processes that occur in nature are classified into two mutually exclusive species: either <strong>deterministic<\/strong> or <strong>indeterministic.<\/strong> A deterministic process is one that, given certain <strong>initial conditions,<\/strong> always leads to the same results. On the other hand, a process is indeterministic when, for the same initial conditions, it can provide a multiplicity of possible outcomes. These possible outcomes, whether unique or multiple, are also known as <strong>states.<\/strong> In turn, processes are understood through models, which are analogously deterministic or indeterministic.<\/p>\n<p style=\"text-align: justify; color: #000000;\">It is in the context of indeterministic processes that <strong>the study of probabilities<\/strong> emerges. This is a <strong>formal science<\/strong> (like <a href=\"https:\/\/toposuranos.com\/category\/ciencias\/matematica\/logica\/\" rel=\"noopener\" target=\"_blank\"><strong>logic<\/strong><\/a>) with which we can extract information about the frequency with which an indeterministic process tends to produce a certain state or set of states.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Deterministic and Indeterministic Processes in Nature<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DsDU0MjD_XY&amp;t=288s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">Suppose we want to model the process of launching a projectile.<\/span><\/strong><\/a> In a controlled environment, <strong>Newton&#8217;s mechanics<\/strong> tell us that for each velocity and initial position, the projectile will have a determined impact point, representing a deterministic model of reality. However, in real life, absolutely controlled environments do not exist, and what we will see is that the projectile tends to fall within a certain region, implying a multiplicity of possible states.<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/basket.jpg\" alt=\"parabolic shot, Deterministic and Indeterministic Processes\" width=\"500\" height=\"500\" class=\"aligncenter size-full wp-image-22067 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/basket.jpg\" alt=\"parabolic shot, Deterministic and Indeterministic Processes\" width=\"500\" height=\"500\" class=\"aligncenter size-full wp-image-22067 lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">It is generally said that our limitations in controlling and measuring both the environment and initial conditions prevent us from determining the final states of a system, forcing us to deal with a multiplicity of them and with non-deterministic models. As a process increases in complexity, so does the lack of control over the environment and initial conditions.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Probabilities and Chance<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DsDU0MjD_XY&amp;t=561s\"><strong><span style=\"color: #d00000;\">Chance is an inherent characteristic of indeterministic processes.<\/span><\/strong><\/a> A process is said to be <strong>random<\/strong> or <strong>chance-based<\/strong> when, for a certain set of initial conditions, none of the possible states seem to occur more frequently than the others. The simplest example is found in the toss of a coin. As the number of tosses increases, it is observed that the frequency with which heads and tails appear tends to be similar. In other words:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{N\\to \\infty} \\dfrac{C}{N} = \\lim_{N\\to \\infty} \\dfrac{S}{N} = \\dfrac{1}{2} <\/span>\n<p style=\"text-align: justify; color: #000000;\">where <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> is the total number of tosses, <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> are the number of heads and tails obtained among the <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> tosses.<\/p>\n<p style=\"text-align: justify; color: #000000;\">This number is the <strong>probability<\/strong> of obtaining heads or tails, and its understanding is obtained by analyzing <strong>experiments with equiprobable outcomes<\/strong>. This is the essence of deterministic and indeterministic processes and their relationship with probabilities and chance.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Deterministic and Indeterministic Processes, Probabilities and Chance SummaryIn this introductory class to Probability Theory, we will explore the connection between deterministic and indeterministic processes and their relationship with probabilities and chance. We will see how processes in nature are classified into two mutually exclusive species and how they are understood through deterministic and indeterministic models. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":25367,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":8,"footnotes":""},"categories":[567,670],"tags":[],"class_list":["post-25368","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","category-probabilities-and-statistics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Deterministic and Indeterministic Processes - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Learn to differentiate between Deterministic and Indeterministic Processes in nature and how they affect our understanding of chance\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/en\/deterministic-and-indeterministic-processes\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Deterministic and Indeterministic Processes\" \/>\n<meta property=\"og:description\" content=\"Learn to differentiate between Deterministic and Indeterministic Processes in nature and how they affect our understanding of chance\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/en\/deterministic-and-indeterministic-processes\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-03-10T00:00:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-05-21T09:45:05+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/DETERMINISTASVSINDETERMINISTAS-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Deterministic and Indeterministic Processes\" \/>\n<meta name=\"twitter:description\" content=\"Learn to differentiate between Deterministic and Indeterministic Processes in nature and how they affect our understanding of chance\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/DETERMINISTASVSINDETERMINISTAS.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/deterministic-and-indeterministic-processes\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/deterministic-and-indeterministic-processes\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Deterministic and Indeterministic Processes\",\"datePublished\":\"2021-03-10T00:00:03+00:00\",\"dateModified\":\"2024-05-21T09:45:05+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/deterministic-and-indeterministic-processes\\\/\"},\"wordCount\":644,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/deterministic-and-indeterministic-processes\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/12\\\/DETERMINISTASVSINDETERMINISTAS.jpg\",\"articleSection\":[\"Mathematics\",\"Probabilities and Statistics\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/deterministic-and-indeterministic-processes\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/deterministic-and-indeterministic-processes\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/deterministic-and-indeterministic-processes\\\/\",\"name\":\"Deterministic and Indeterministic Processes - 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