tag:blogger.com,1999:blog-22973357.post3230720953924684059..comments2023-09-27T07:44:19.769-04:00Comments on Sabine Hossenfelder: Backreaction: What are Differential Equations and how do they work?Sabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger16125tag:blogger.com,1999:blog-22973357.post-92017688492794980512020-10-22T23:32:09.440-04:002020-10-22T23:32:09.440-04:00While what you say is correct, this is not the cas...While what you say is correct, this is not the case for the differential equations that we use in the foundations of physics, the Schroedinger equation (linear, first order), and Einstein's Field Equations (on whose initial value problem much ink has been spilled). Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-53346624632630096302020-10-22T12:57:42.827-04:002020-10-22T12:57:42.827-04:00A couple of mathematical points connected with the...A couple of mathematical points connected with the article above, which should be considered before drawing philosophical conclusions (e.g. about determinism, etc):<br /><br />(1) The standard Cauchy/Peano theorem on differential equations only guarantees existence of a solution; it does not guarantee uniqueness.<br /><br />(2) Differential equations exist which have solutions, but have no Royhttps://www.blogger.com/profile/18331240261199344334noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-53248136279069284272020-10-13T02:52:14.256-04:002020-10-13T02:52:14.256-04:00On free will:
"My will is wet *) said Winnif...On free will:<br /><br />"My will is wet *) said Winnifred and pulled her husband into bed"(John O'Mill).<br /><br />*) law.martenhttps://www.blogger.com/profile/02423871089614417690noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-34017051240632992982020-10-10T12:25:40.651-04:002020-10-10T12:25:40.651-04:00Determinism has implications for computational iss...Determinism has implications for computational issues. Consider AI: our brains are running the deterministic "I" program. So why not AI? The answer hinges on whether the "I" program can be implemented on some other device. And what sort of algorithm? Is any implementation of the "I" program computationally intensive (no efficient shortcut) or not? For that matter, Rick Lubbockhttps://www.blogger.com/profile/01070357751075383393noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-21737289386246832552020-10-05T09:56:31.882-04:002020-10-05T09:56:31.882-04:00In first year physics, we hit two high points - th...In first year physics, we hit two high points - the damped driven harmonic oscillator in mechanics, and the RLC circuit in electricity and magnetism. 'This is the same differential equation as we saw last term' was a moment of triumph. DougOnBloggerhttps://www.blogger.com/profile/16411970226629138387noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-3659189398880271532020-10-05T02:28:30.279-04:002020-10-05T02:28:30.279-04:00Hi Sabine,
Should I understand that the constant...Hi Sabine,<br /> <br />Should I understand that the constants of nature (and all free parameters) may be symptoms of the reign of differential equations ? or of inability to describe/imagine/understand a lower level dynamics ? <br /><br />Best,<br />J. akidbellehttps://www.blogger.com/profile/12292741599925116131noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-52803137375954491012020-10-04T22:06:41.191-04:002020-10-04T22:06:41.191-04:00I am having a terrible mental block when it comes ...I am having a terrible mental block when it comes to differential equations. I can pick one out n a crowd, but I don't know what gives rise to them. That is, I don't know why so many systems are expressed as a differential equation. And I am very suprised that many solutions to differential equations involve euler's number e.Manly Geekhttps://www.blogger.com/profile/00221268360981218814noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-40750362202262857902020-10-04T11:41:57.314-04:002020-10-04T11:41:57.314-04:00I am a little disappointed that the post did not m...I am a little disappointed that the post did not mention finite-difference equations. I had a calculus course in high school and a couple in college, and only learned about finite-difference equations in a job-related Masters program. It had a significant effect on my world view. (From a world of infinities everywhere to one of vast but discrete systems.) <br /><br />They are similar in form and JimVhttps://www.blogger.com/profile/10198704789965278981noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-88880178939374485062020-10-04T08:28:17.225-04:002020-10-04T08:28:17.225-04:00The greatest danger in fore-casting or post-castin...The greatest danger in fore-casting or post-casting with differential equations is illustrated by that parabolic arc.<br />Given three points on a parabolic arc we can compute the initial conditions and values forward or backward in time indefinitely; but try this with the arc of a projectile. Post cast far enough, and it claims the missile was at some time in the past miles beneath the earth. Dr. A.M. Castaldohttps://www.blogger.com/profile/17988116835722393503noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-14401165421917635402020-10-04T05:18:16.339-04:002020-10-04T05:18:16.339-04:00“If I tell you how many people are ill today, you ...“If I tell you how many people are ill today, you can calculate how many will be ill next week.”<br />It should work also in the other direction of time: If I tell you how many people are ill today; you can calculate how many were ill last week. Unfortunately, this does not work. The constant in the equation is not constant. It changes with time. Why? Because it is my free will to decide whether Henning Flessnerhttps://www.blogger.com/profile/12666705848468595906noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-16657228774099735922020-10-03T15:33:19.440-04:002020-10-03T15:33:19.440-04:00On the one hand one can marvel that a formal mathe...On the one hand one can marvel that a formal mathematical structure can model the behavior of "stuff" so well. On the other hand, we realize that these differential equations are the product of a brain, made out of "stuff". So if the "stuff" has certain properties, those properties are expressed by anything made out of that "stuff". So math isn't an Rick Lubbockhttps://www.blogger.com/profile/01070357751075383393noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-47007348226750780002020-10-03T15:16:46.596-04:002020-10-03T15:16:46.596-04:00So next week it will be more about philosophy than...So next week it will be more about philosophy than about physics. I don’t mind.Mark Behetshttps://www.blogger.com/profile/10357707342209728359noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-25137439904166132662020-10-03T14:16:01.066-04:002020-10-03T14:16:01.066-04:00I learned about differential equation in high scho...I learned about differential equation in high school. In particular it was the simple dx/dt = ax. With the calculus I understood this lead to dx/x = adt and the left is a log and the right is just at and you get the exponential. I thought this was pretty nifty. Then of course this gets generalized to many differential equations, and in particular partial differential equations.<br /><br />It is Lawrence Crowellhttps://www.blogger.com/profile/12090839464038445335noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-78343912557116397042020-10-03T12:06:56.798-04:002020-10-03T12:06:56.798-04:00Understanding maxwell equations of electromagnetis...Understanding maxwell equations of electromagnetism was what motivated me to study calculus and physics and eventually go to college. I'm a third year mechatronics engineer student now.<br /><br />I just wanted to come by and say that your videos and Matt's (from PBS space time) really motivated me to try and dive a little deeper into QM, specially your video about bra-ket notation. <br /Viniciushttps://www.blogger.com/profile/13850818401542524952noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-79098594976632492882020-10-03T11:40:38.612-04:002020-10-03T11:40:38.612-04:00I'm neither a physicist nor a statistician, bu...I'm neither a physicist nor a statistician, but I've worked at times in the operations research field, where practitioners select models that best reflect, say, the rate at which to replace tires in a vehicle fleet before they fail. The impression I have is that they go to a fairly limited set of available differential equations that, when the variables are plugged in, give a "close John Brucehttps://www.blogger.com/profile/04625895756906828468noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-79552978077804067202020-10-03T11:04:26.971-04:002020-10-03T11:04:26.971-04:00Sabine wrote: "you want to know how N will ch...Sabine wrote: "you want to know how N will change in time"<br /><br />In this case, N being an integer, it cannot be described by a differential equation. Of course you are aware of that. Some people frequently forget that differential equations are not an exact representation of reality, but only of <b>averages</b> (or probabilities).<br /><br />> "a piece of mathematics Wernerhttps://www.blogger.com/profile/08502954437062856468noreply@blogger.com