tag:blogger.com,1999:blog-8148573551417578681.post8082703920897642231..comments2021-02-25T08:33:09.257-08:00Comments on Dark Buzz: Randomness cannot be empirically shownRogerhttp://www.blogger.com/profile/03474078324293158376noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8148573551417578681.post-39713870834988093732020-02-18T23:15:04.706-08:002020-02-18T23:15:04.706-08:00Correct. Randomness is an abstract, mathematical n...Correct. Randomness is an abstract, mathematical notion that does not directly exist. <br /><br />The idealization involved in the concept of randomness starts from the idea of an absence of *some* form of order, and then, in the limit, it goes to the idea of an absence of *every* form of order. <br /><br />Taken in this ``purest'' form, randomness is a purely mathematical concept; it is a concept of method alone. It cannot concretely exist for a similar set of reasons that objects of zero or infinite size cannot.<br /><br />Thus, first, it's best to begin with relative degrees of randomness. <br /><br />For instance, a complete polynomial of degree 7 is more complex than another with a degree 3. Hence, predicting the next number in a discrete data-series generated using a 7-degree polynomial, is more difficult; it takes more computational effort; the data series generated shows less order in the successive numbers. Hence, we can say that a 7-degree polynomial-generated series shows more randomness than a 3-degree one. <br /><br />From this viewpoint, generation of a purely random sequence would require an infinite-degree polynomial. <br /><br />Those who say that perfect randomness *physically* exists---whether at the level of stat. mech. or QM, or QFT---are welcome to keep themselves engaged with infinite-degree polynomials, and shut their mouth up in the meanwhile. <br /><br />(Guess the same argument can also be made using the Fourier transform, but polynomials are simpler, and I guess, equally powerful (if not more) for the purpose.)<br /><br />Best,<br />--Ajit<br />Ajit R. Jadhavhttps://ajitjadhav.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-26184664121520283892020-02-17T15:30:18.919-08:002020-02-17T15:30:18.919-08:00It is a strange day for irony, when one can use an... <br />It is a strange day for irony, when one can use an argument that basically goes:<br /> "If only I knew EVERYTHING about something then I could have certainty in my randomness." <br /> ... and keep a straight face. <br /><br />Roger, the man you love to ridicule had it right.<br /><br />" ... as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."<br />Geometry and Experience, Lecture before the Prussian Academy of Sciences, January 27, 1921<br /><br />CFTnoreply@blogger.com