tag:blogger.com,1999:blog-6837159629100463303.post3662680724290404383..comments2023-06-18T01:25:08.748-07:00Comments on Information Transfer Economics: An information transfer traffic modelJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-6837159629100463303.post-17102190678168826252014-12-19T11:43:59.470-08:002014-12-19T11:43:59.470-08:00Thanks, that helps. I also have typo's!Thanks, that helps. I also have typo's!Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-19937193876586030882014-12-19T10:45:38.306-08:002014-12-19T10:45:38.306-08:00Hi Roger, I think there is a typo in that equation...Hi Roger, I think there is a typo in that equation above. However, the relationship between X and T follows from solving the differential equation, which yields<br /><br />X ~ T^(1/k)<br /><br />Squaring both sides yields<br /><br />X^2 ~ T^(2/k)<br /><br />It's a homogeneous differential equation of first order and can be solved by separation of variables:<br /><br />dX/dT = X/(k T)<br /><br />dX/X = dT/(k T)<br /><br />log X ~ (1/k) log T<br /><br />X ~ T^(1/k)Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-37928706213745691732014-12-19T07:24:13.241-08:002014-12-19T07:24:13.241-08:00As I study this, I think to myself that we have tw...As I study this, I think to myself that we have two scales (we could think of 'rulers') of different size intervals. In your examples, one scale is marked in units of distance, the other in units of time. The ratio between scale units is V = dX/dt.<br /><br />Next, we insert an object and undertake the task of measuring it in both scales. We will get one measurement for each scale, a total of two measurements. One measurement will be X and the second T.<br /><br />Now we can relate the two scales by the relationship<br /><br />V = dX / dt = X / kT where k is a proportionality constant unique to the item measured.<br /><br />Moving to the diffusion process, I envision X and T each transferred to a paper chart to be represented as a square, X x X and T x T. To scale them so that each paper size was identical, we would scale X = kT * V. Finally, we could find the area of the square using both scales to find that<br /><br />X^2 = (kT * V)^2<br /><br />This does not agree with your<br /><br /> X^2 ~ T^(2*k)<br /><br />so I must not be understanding something correctly.<br /><br /><br /><br />Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-68264938721976040112014-12-13T10:25:21.025-08:002014-12-13T10:25:21.025-08:00I added a few statements in brackets in the post a...I added a few statements in brackets in the post above to show the information equilibrium viewpoint.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-64414774403783835002014-12-12T16:02:19.564-08:002014-12-12T16:02:19.564-08:00A quick way to see the information equilibrium:
I...A quick way to see the information equilibrium:<br /><br />In equilibrium, the information entropy in the occupied position slots must be equal to the information entropy in the occupied time slots.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.com