tag:blogger.com,1999:blog-22973357.post8567004409307256888..comments2023-09-27T07:44:19.769-04:00Comments on Sabine Hossenfelder: Backreaction: The Complex PlaneSabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger23125tag:blogger.com,1999:blog-22973357.post-78963304946695127662007-10-08T15:29:00.000-04:002007-10-08T15:29:00.000-04:00okay, thanks, if that was the problem then I misun...okay, thanks, if that was the problem then I misunderstood the question. But he seems to know this answer, so I don't get where the problem is?Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-16413584860853558482007-10-08T15:26:00.000-04:002007-10-08T15:26:00.000-04:00The answer to Neil's question is a countable infin...The answer to Neil's question is a countable infinity of points that is dense on the unit circle.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-25353488930710164952007-10-08T15:19:00.000-04:002007-10-08T15:19:00.000-04:00Neil is asking what points on the circle represent...Neil is asking what points on the circle represent unity to the power of an irrational number.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-57040253521792811592007-10-08T13:50:00.000-04:002007-10-08T13:50:00.000-04:00Neil, I understand your question but you didn't un...Neil, I understand your question but you didn't understand my answer. The 'normal' definition for sqrt doesn't help you because you need a sensible definition in the complex plane, I have given you the appropriate one above. I have also explained that these solutions lie on different branches of the ln and not actually in the same plane. You can find all of this in any textbook on functional Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-27346456978014469802007-10-08T13:44:00.000-04:002007-10-08T13:44:00.000-04:00Bee, the number in the exponent was meant to be th...Bee, the number in the exponent was meant to be the normal definition, so that would be around 0.7071... The ambiguity was supposed to be in the full solution set for expression of 1^0.7071... not in the number giving the exponent itself. The trouble is, 1^(707/1000) should have 1000 roots, 1^(7071/10,000) should have 10,000 roots (per my straightforward argument earlier) and so on, to "Neil Bateshttps://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-52368867347971406342007-10-07T22:02:00.000-04:002007-10-07T22:02:00.000-04:00Hi Bee, first thing that comes to mind here, your ...Hi Bee, first thing that comes to mind here, your missing Stefan!<BR/><BR/>This definately rates the best notepad "doodling", I have come across, littered with sexual Innuendo's ?<BR/><BR/>Stefan is on your notepad as well as your mind? ;)<BR/><BR/>best wishes to you both, paul.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-89327051024808933602007-10-07T17:10:00.000-04:002007-10-07T17:10:00.000-04:00"perfectly meaningful exponent 1^(sqrt 0.5)"Well, ...<I>"perfectly meaningful exponent 1^(sqrt 0.5)"</I><BR/><BR/>Well, for it to be perfectly meaningful you'll have to define it, and it's not clear to me what you actually mean, i.e. what is your definition for sqrt in the complex plane. The general definition for z^w goes via the logarithm as exp(w*ln(z)). What you are asking for is a solution to the equation z^something = exp ( something* ln(z) )Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-82016172413680336682007-10-07T16:37:00.000-04:002007-10-07T16:37:00.000-04:00OK, the psych graph is interesting, but the roots ...OK, the psych graph is interesting, but the roots of unity involve a very real problem IMHO:<BR/>There are n nth roots of unity, right? That also means, four roots for 1^(3/4) etc. (ie, the four fourth roots of unity each taken to the third power, so (1, -1, i, -i) each to the third, and so for the roots of 1^(7/23) etc. So, what are the roots of the perfectly meaningful exponent 1^(sqrt 0.5) etcNeil Bateshttps://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-33444392203604638372007-10-07T09:07:00.000-04:002007-10-07T09:07:00.000-04:00Hi CIP, Hi Arun,Yes, the positive real axis doesn'...Hi CIP, Hi Arun,<BR/><BR/>Yes, the positive real axis doesn't say 'reality' but 'realism', I was thinking about it much like Cynthia says, being trapped in a wheel pulled to all sides. The positive real axis is probably the way to go? <BR/><BR/><I> I don't get "reality is no thing" unless it means "no single thing".</I><BR/><BR/>It's probably impossible to get it without actually reading the fullSabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-14435006873184567422007-10-06T21:40:00.000-04:002007-10-06T21:40:00.000-04:00Which explains "It is clear, then, that the term '...Which explains <I>"It is clear, then, that the term 'reality' (which in this context means 'reality as a whole') is not properly to be regarded as part of the content of thought. Or, to put this in another way, we may say that reality is no thing and that it is also not the totality of all things, i.e. we are not to identify 'reality' with 'everything'."</I><BR/><BR/>Optimism, pessimism are part Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-36236585279466513362007-10-06T21:37:00.000-04:002007-10-06T21:37:00.000-04:00CIP,Optimism and pessimism are states of mind, not...CIP,<BR/><BR/>Optimism and pessimism are states of mind, not of reality. I think Bee is quite correct.Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-14532803384019434892007-10-06T15:56:00.000-04:002007-10-06T15:56:00.000-04:00see -> seem, I meant.see -> seem, I meant.CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-61754920480479316702007-10-06T15:54:00.000-04:002007-10-06T15:54:00.000-04:00Bee,It worries me that both your optimism and pess...Bee,<BR/><BR/>It worries me that both your optimism and pessimism see equally unrealistic ;)CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-56910055671194531842007-10-06T14:37:00.000-04:002007-10-06T14:37:00.000-04:00Uncle Al, I guess imaginary numbers are a bit shro...Uncle Al, I guess imaginary numbers are a bit shrouded in secrecy... And if I'm reading you right, I completely agree that this couple standing back-to-back is trapped in a complex wheel, appearing as though they're in a medieval torture chamber of sorts!;~)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-10983281317971064612007-10-06T13:53:00.000-04:002007-10-06T13:53:00.000-04:00Mersenne PrimeIt looks as though primes tend to co...Mersenne Prime<BR/><BR/><A HREF="http://photos1.blogger.com/x/blogger/6460/633/320/473723/3.png" REL="nofollow">It looks as though primes tend to concentrate in certain curves that swoop away to the northwest and southwest, like the curve marked by the blue arrow. (The numbers on that curve are of the form x(x+1) + 41, <B>the famous prime-generating formula discovered by Euler in 1774.</B>)</A><PlatoHagelhttps://www.blogger.com/profile/00849253658526056393noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-73430384785223031652007-10-06T11:57:00.000-04:002007-10-06T11:57:00.000-04:00Hahahaha! I'm totally going to print this out on a...Hahahaha! I'm totally going to print this out on a ferromagnetic backing and use it like a <A HREF="http://www.amazon.com/Feeling-Today-Smiley-Faces-Poster/dp/B0000VI28G" REL="nofollow">"how are you feeling today?"</A> poster. :)Aaronhttps://www.blogger.com/profile/18281785407407667986noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-58857691475109720482007-10-06T11:47:00.000-04:002007-10-06T11:47:00.000-04:00There you go giving Bush the Lesser ideas for his ...There you go giving Bush the Lesser ideas for his many <I>sub rosa</I> European torture prisons. As they say in the US Department of Justice,<BR/><BR/>"Albanians gotta eat too!"Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-78282355600053110312007-10-06T09:53:00.000-04:002007-10-06T09:53:00.000-04:00Hi Rae Ann: I meant to add a minimum of explanatio...Hi Rae Ann: I meant to add a minimum of explanation, but I was too tired yesterday. <B>R</B> is the 'Real' axis (where all the numbers are you find on your bank statement), <B>I</B> is the Imaginary axis. You introduce it so you can solve all polynomial equations (the equation x^2 = -1 does not have a solution in <B>R</B> but on <B>I</B>). If you draw a vector in the plane from the origin to the Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-817869021090589242007-10-06T09:35:00.000-04:002007-10-06T09:35:00.000-04:00You guys are too smart for me!You guys are too smart for me!Rae Annhttps://www.blogger.com/profile/10239791074376508016noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-48195885324258476402007-10-06T09:27:00.000-04:002007-10-06T09:27:00.000-04:00Isn't Im(Fantasy) \neq 0 ?Isn't Im(Fantasy) \neq 0 ?Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-3536661113254821852007-10-06T08:26:00.000-04:002007-10-06T08:26:00.000-04:00I like it. Hmm, I'm not sure "Fatalism" is best f...I like it. Hmm, I'm not sure "Fatalism" is best for the negative real axis though. Maybe "Fantasy"?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-21179348001097216482007-10-06T08:16:00.000-04:002007-10-06T08:16:00.000-04:00I'm not in an eigenstate, and my overall phase is ...I'm not in an eigenstate, and my overall phase is non-observable anyway ;-)Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-81854842204186614382007-10-06T07:48:00.000-04:002007-10-06T07:48:00.000-04:00I guess many people feel pushed into this complex ...I guess many people feel pushed into this complex plane simple exp(iwt). This drawing begs the question : In which phase are you ?Anonymousnoreply@blogger.com