tag:blogger.com,1999:blog-6837159629100463303.post3368739464087488407..comments2023-06-18T01:25:08.748-07:00Comments on Information Transfer Economics: In defense of equilibriumJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger16125tag:blogger.com,1999:blog-6837159629100463303.post-7492564555192590152014-07-15T14:14:30.087-07:002014-07-15T14:14:30.087-07:00Again, I would refer you to this post
http://noah...Again, I would refer you to this post<br /><br /><a href="http://noahpinionblog.blogspot.com/2013/02/is-business-cycle-cycle.html" rel="nofollow">http://noahpinionblog.blogspot.com/2013/02/is-business-cycle-cycle.html</a><br /><br />But yes. For example DSGE stands for "dynamic stochastic general equilibrium", which is one of the major ways economist tackle economic systems. See for example here:<br /><br />http://www.federalreserve.gov/pubs/feds/2010/201026/<br /><br />Even older models like P* are "dynamic math" as you put it:<br /><br />http://www.oecd.org/eco/outlook/34254867.pdf<br /><br />Do you honestly think that economists didn't know or somehow just forgot about basic calculus from the 1700s?<br /><br />This reference starts from stochastic differential equations that are somewhat more recent, dating from 1900:<br /><br />http://epubs.siam.org/doi/pdf/10.1137/1015001Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-21513051287867757492014-07-15T13:40:11.884-07:002014-07-15T13:40:11.884-07:00Have you seen very much economics done with dynami...Have you seen very much economics done with dynamic math? Math that can produce cycles with out external driving functions?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-69681923761472749702014-07-15T10:49:49.926-07:002014-07-15T10:49:49.926-07:00I suggest you read this:
http://noahpinionblog.bl...I suggest you read this:<br /><br />http://noahpinionblog.blogspot.com/2013/02/is-business-cycle-cycle.html<br /><br />Equilibrium in economics has nothing to do with equilibrium in mechanics. (If it was, it would be more well defined!)Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-63318372644281322832014-07-14T21:00:54.369-07:002014-07-14T21:00:54.369-07:00in 1 the verbage should have been
X(t)=a sin( sq...in 1 the verbage should have been <br /><br />X(t)=a sin( sqrt(K/M)*t ) ,as the solution.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-24771950655255984982014-07-14T20:56:59.075-07:002014-07-14T20:56:59.075-07:00This would actually you alot:
I would have more s...This would actually you alot:<br /><br />I would have more simply given:<br /><br />1. F(X)= X"(t)M= -KX(t) as the ODE, (where X" is d/dt d/dt X.)<br /> K as spring constant, M is mass.<br /> <br /><br /> X(0)=a ,X´(0)=0 ,as the initial condions of position and inital velocity=0.<br /> X(t)=a sin( sqrt(K/M)*t ) ,and the solution where. <br /><br /> <br /> I am totally snowed probably as intended for your answer for number 1. I suspect it has nothing to do with a physical elastic spring?<br /><br /> exp(-iHt) term looks like it might be mathematical oscillation of some sort. I do not understand the notation.<br /><br />2. I would have given this, Your equation would have been able to give this one with a G in it. <br /><br /> F(R)= M R"=-(GMm)/Mag(R)¨2 UnitVector(R)<br /> The vector initial conditions would be R(t0) and R´(t0).<br /><br />A nifty application for your more general equation is used in structures under a different name.<br /><br />"You are incorrect in referring to a harmonic oscillator being a "non-equilibrium" situation. Dynamic is not the opposite of equilibrium; dynamic is the opposite of static."<br /><br />I was using a more basic and common (high school) definition of "mechanical equilibrium." More like static momentum (and in this case velocity ). Which the oscilator would not be in equilibrium while oscilating and the satelite would not be for eliptical orbits even though the orbit would be stable. ( I had a math teacher tell the class there are many definitions of equilibrium.) It is interesting to learn of a more theoretical definition of "equilibrium". But that definition does not negate the other one.<br /><br />http://en.wikipedia.org/wiki/Mechanical_equilibrium<br /><br />"Both a stable orbit and a harmonic oscillator represent equilibrium solutions " <br /><br />When I googled "equilibrium solutions" I got some thing I was more familiar with. Such as in the first figure. In this case the equilibrium solutions are static.<br /><br />http://tutorial.math.lamar.edu/Classes/DE/EquilibriumSolutions.aspx Text search for "equilibrium solution". This equilibrium is arrived at by doing the dynamic math, not assuming the equilibrium first. <br /><br />"But again the solution for a stable orbit is an equilibrium solution (the time average of its energy is constant q.v. the virial theorem)." That a new and interesting theorem to me but an average over time looses the dynamics in time. <br /><br />"The most familiar non-equilibrium situation in the sense of the post above is a pot of boiling water." That is a very good contrasting example for more theoretically abstract definition of (non)equilibruium you have used.<br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-87251790500689924362014-07-14T19:00:19.295-07:002014-07-14T19:00:19.295-07:00non-HTML HTML fail
| α > = Σ | n > < n |...non-HTML HTML fail<br /><br />| α > = Σ | n > < n | α ><br /><br />< n | exp(iH*t) H exp(-iHt) | n > = < n | H | n > = (n + 1/2) < n | n >Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-79650515850831880772014-07-14T18:55:56.144-07:002014-07-14T18:55:56.144-07:00You are incorrect in referring to a harmonic oscil...You are incorrect in referring to a harmonic oscillator being a "non-equilibrium" situation. Dynamic is not the opposite of equilibrium; dynamic is the opposite of static. Both a stable orbit and a harmonic oscillator represent equilibrium solutions in the sense of the post above ... their time average of the energy is constant.<br /><br />This will actually help you a lot:<br /><br />H = N + 1/2<br /><br />|α> = Σ |n><br /><br />|α(t)> = exp(-iHt)|α(0)><br /><br /> = <br /><br /> = = (n + 1/2)<br /><br />i.e. the energy of a harmonic oscillator is constant, which means it is an equilibrium in the sense of equilibrium we are talking about in the post above.<br /><br />For the second question:<br /><br />L = p^2/2m - M m/q<br /><br />d/dt ∂L/∂pi - ∂L/∂qi = 0<br /><br />But again the solution for a stable orbit is an equilibrium solution (the time average of its energy is constant q.v. the virial theorem).<br /><br />The most familiar non-equilibrium situation in the sense of the post above is a pot of boiling water.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-10460085247963360012014-07-14T17:58:37.562-07:002014-07-14T17:58:37.562-07:00Come on. Its easy. Please do not deflect the ques...Come on. Its easy. Please do not deflect the question.<br /><br />Hint F(x)=.... or F(R)=....Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-32864887107063104932014-07-14T15:05:37.617-07:002014-07-14T15:05:37.617-07:00Should read
"They should be quite easy for ...Should read <br /><br />"They should be quite easy for you to answer quickly." <br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-89178418735732211252014-07-14T14:59:34.526-07:002014-07-14T14:59:34.526-07:00Yes, it is a test. The very basics!
They shoul...Yes, it is a test. The very basics! <br /><br />They should be quite easy and quickly for you to answered.<br /><br />In addition, they are two examples of dynamic (non-equilibrium) situations most people can picture. <br /><br />Basics with broader applications to economics. (I must admit that I am having a hard time understanding the information theory stuff.)<br /><br /><br /><br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-14295923582460961502014-07-14T14:24:29.712-07:002014-07-14T14:24:29.712-07:00I defend equilibrium because when I go to the supe...I defend equilibrium because when I go to the supermarket the price of my favorite Irish whiskey is about 25 dollars each and every week :)<br /><br />That's equilibrium! *hic*Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-66342059302463447372014-07-14T14:18:26.963-07:002014-07-14T14:18:26.963-07:00Is this some kind of test? Hilarious. How about yo...Is this some kind of test? Hilarious. How about you read my thesis:<br /><br />http://arxiv.org/abs/nucl-th/0508036<br /><br />If you can remotely tell me what it is about, I'll answer your questions :)Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-67233263168914665652014-07-14T13:15:09.752-07:002014-07-14T13:15:09.752-07:001. What is the ODE equation of the movement of a ...1. What is the ODE equation of the movement of a mass connected to a spring. Virticle or horizontal your choice. You may neglect friction forces if you like. (Also, the spring is streached out such that its loops do not ever touch in compression.)<br /><br />ODE, ordinary differential equation?<br /><br />What is one solution to the ODE, and the initial conditions?<br /><br /><br />2. What is the vector ODE equation for a satelite orbiting the earth. What would be the initial conditions. No solution requested?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-83527411775662126072014-07-14T12:59:00.470-07:002014-07-14T12:59:00.470-07:00I do do not know why you defend economists and equ...I do do not know why you defend economists and equilbriom rather than pushing dynamics.<br /><br />Do you not want them on your more fertile lawn?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-34993372763372032952014-07-14T12:47:19.704-07:002014-07-14T12:47:19.704-07:00I have a phd in physics (I'm a theoretical par...I have a phd in physics (I'm a theoretical particle physicist by training -- quantum field theory, string theory and such, but now I'm more of a rocket scientist -- I've stood at the top of an Atlas V rocket prepped for launch).<br /><br />I'll happily admit I have no training in economics :)Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-53515494670145227242014-07-14T12:25:36.472-07:002014-07-14T12:25:36.472-07:00Have you compleated more than 4 lab classes in qua...Have you compleated more than 4 lab classes in quantitative science or engineering courses? <br /><br />Have you compleated any degrees in physics? If so, which ones (BS,MS,or Piled Higher and Deeper)?<br /><br />What about economics?<br /><br /><br />Anonymousnoreply@blogger.com