{"id":1027,"date":"2020-04-24T23:30:33","date_gmt":"2020-04-25T03:30:33","guid":{"rendered":"http:\/\/aristotle2digital.blogwyrm.com\/?p=1027"},"modified":"2020-06-06T07:55:59","modified_gmt":"2020-06-06T11:55:59","slug":"what-is-random","status":"publish","type":"post","link":"https:\/\/aristotle2digital.blogwyrm.com\/?p=1027","title":{"rendered":"What is Random"},"content":{"rendered":"\n

Call it happenstance or blind luck but we all have a\nnotional idea of randomness and the role it plays in our lives.  We see learned authorities invoke random\nprocesses in Darwin\u2019s theory of natural selection, in the vicissitudes of the\nStock Market, or in the efficacy of a pharmaceutical in treating an ailment or\ndisease.  Surprisingly, a precise\ndefinition of random is often elusive and controversial.  Despite the very nature of randomness<\/a>, this post will\ntry to proceed deterministically through some of the discussions over the\nmillennia starting with the bigger questions and ending with the smaller ones.  Interestingly, there are deep connections\nbetween the smallest and largest questions that often sneak up.<\/p>\n\n\n\n

At the top of the list is the very question about free will versus\ndeterminism.  If free will exists then\nrandom outcomes are possible but, conversely, if the universe\u2019s evolution is\npredetermined then every outcome is part of a larger plan and only our own\n(predetermined) ignorance prevents us from perceiving it.  Much of the thinking here falls under the problem of\nfuture contingents<\/a>.  One of the first\nphilosophical scenarios used to explore future contingencies was Aristotle\u2019s\nexample of the sea battle <\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

that may or may not be fought tomorrow.  Assume, for a moment, that the proposition\n\u2018the sea battle will be fought tomorrow\u2019 is unequivocally true.  Next, let\u2019s turn our face from the future and\nconsider the past.  If the proposition \u2018the\nsea battle will be fought tomorrow\u2019 is true today, then it was also true yesterday\nbecause the proposition\u2019s truth value in the past was also resolved and locked\nin.  If it was true yesterday then it\nmust also have been true the day before and so on.  The same holds if the proposition \u2018the sea\nbattle will not be fought tomorrow\u2019 is true. \nThe actual proposition is not at all important but rather that the truth\nvalue of a given future event is certain. At this point we are forced to note\nthat if a future event has a well-defined truth value then free will and\/or\nrandomness cannot be allowed. Free will of the combatants would afford them the\nability to cancel the battle while a random event, say an unforeseen terrible\nstorm, may arise and prevent one navy from arriving.<\/p>\n\n\n\n

To get around the problem that a future proposition must\nhave a definite state of true or false like current propositions do, Aristotle\ncreated a third truth value for future events that regards them neither true\nnot false but being contingent.  This is\nthe only violation of the law of the excluded middle that Aristotle\nallows.  Philosophers seem to love to\nargue about this (e.g., see the introduction to The Problem of Future Contingents<\/em> by Richard Taylor, originally\npublished in The Philosophical Review,<\/em>\n66 (1957), now accessibly reprinted in Philosophy\nfor the 21st<\/sup> Century: A Comprehensive Reader<\/em>, edited by Steven\nM. Cahn).  <\/p>\n\n\n\n

The interesting thing is that while philosophers argue over\nhow well Aristotle\u2019s argument addresses the problem of future contingents and\nall the concepts that flow from it (particularly randomness), mathematicians,\nengineers, and scientists have all assumed that the randomness is inherent in\nreality.  For example, in a recent paper\non Bell\u2019s Theorem and random\nnumbers<\/a>, Pironio et al start by saying \u201cRandomness is a fundamental feature\nof nature\u2026\u201d already assuming, as a given, an ontological position still\nwrestled over by philosophers. <\/p>\n\n\n\n

Of course, the very roots of probability theory date back to\nthe 17th<\/sup> century and often centered on characterizing the randomness\nseen in games of chance. Indeed, it is hard to find any general text on the\nsubject without encountering a coin flip, a dice roll, or the standard deck of\ncards.  The concept of the random\nvariable doesn\u2019t seem to have taken clear shape until the 19th<\/sup>\ncentury when the ideas of probability and expectation value were systematically\nexpressed.  It isn\u2019t easy to get a clear\nand firm history\non the flow of ideas in this field<\/a> and nailing down who contributed what\nand when is a task best left to others.  <\/p>\n\n\n\n

The subject then jumped into overdrive in the 20th<\/sup>\ncentury with ideas being applied to so many things it is hard to keep\ntrack.  The importance of randomness and\ndecision making in the face of uncertainty became central focal points in both\neconomics, control theory, and artificial intelligence.  A variety of distributions were invented and\ncontinue to be invented for understanding experimental data, for actuarial\nsciences and the setting of premiums in insurance, and for predicting the\nreliability and lifetimes of manufactured goods.  The concepts algorithmic\ncomplexity\/randomness and random signals grew in the fields of computer science\nand electronics.  The field of dynamical\nsystems changed how we look at random behavior in systems that exhibit\nchaos.  Perhaps, the single most\ninfluential development was the theory of quantum mechanics, which is\ncompletely deterministic in it predictions right up to but not including\nmeasurement at which point randomness and probability come straight to the\nfront.  <\/p>\n\n\n\n

All that being said, one of the more interesting corners of\nthe modern aspects of randomness is the generation of sequences of random numbers\nfor a variety of computer applications. \nPsuedo-random number generators (PRNG) typically deliver the sequences\nused in simulations of what we believe to be random effects in nature (usually\nunder some guise of the Monte Carlo method). \nHowever, anyone who has used PRNGs professionally soon comes to suspect\ntheir performance in large-scale simulations since they are really periodic\nalgorithms whose short-term manifestation \u2018looks\u2019 random.  In more recent years, rRANDOM.ORG<\/a> has been producing random\nnumbers based on what many believe are ontologically random events in nature\n(in this case atmospheric noise).  The\nfigure below shows a comparison between a set of uniform and normally\ndistributed random numbers (top and bottom, respectively) produced in numpy and\ngenerated by random.org (left and right, respectively).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

To the naked eye they look similar.  Both systems produce \u2018open spot\u2019 and \u2018clumps\u2019\njust as one would expect from a random process. \nBut the gap between looking good and being good is wide and crossing it\nis difficult.  RANDOM.ORG\u2019s page on randomness<\/a>\nor the Wikipedia article on tests for randomness<\/a>\ndetail the various struggles constructing adequate tests but the long and short\nof it is that the difficulty lies in the fact that after millennia of talking\nabout chance versus fate we still know far too little about how the world\nworks. <\/p>\n","protected":false},"excerpt":{"rendered":"

Call it happenstance or blind luck but we all have a notional idea of randomness and the role it plays in our lives.  We see learned authorities invoke random processes… Read more ><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1027","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts\/1027","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1027"}],"version-history":[{"count":0,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts\/1027\/revisions"}],"wp:attachment":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1027"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1027"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1027"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}