In "Running Money" I came across this excerpt which is relevant to something Horselover Fats posted on Wed, 20 Oct 2004 12:06:40
Kessler writes, ================================================== "The guy who told me he looked at only the second derivative of industrial production was onto something. Because information is distributed in milliseconds, there is no time advantage anymore. You have to be ahead of news. You have to look not at change but at how fast change is changing. Your old calculus teacher would remind you, the first derivative is speed. The second derivative is acceleration. There are so many barriers to change. Some are technical, some are based on silly government regulations. But who cares - barriers are barriers. As long as you can find a barrier to invest against, you can make money when the barrier breaks, when change accelerates. Most hedge fund guys take the other side of a trade when they know something no one else does, i.e., investing because others don't know. That's their edge. When you think long-term, the edge is really investing because others *can't* know. I suppose others could know if they thought hard enough, but, oddly, no one does. It's not the actual declining cost of power or transportation, chips or bandwidth, etc., that is hard to figure out. It's the change they enable. These concepts are hard to grasp. It's that nasty second derivative stuff. It's not the amount of change, but the change in the rate of change. Confused? Me too. It's why there are few physicists and why people quit science after high school. It's just too hard to think about. >From the side of the highway, you can't tell which cars are going a constant speed and which are accelerating. But from inside the car, you can feel the seat press against you when you gun it. That's probably the first lesson I learned: to do well, you've got to be in the car, not on the sidelines watching." ================================================== Quite so. And now let's proceed to the epic "Horselover Fats Rides Again" Horselover wrote:-. ================================================== Also, you mentioned Jerk and Jounce ( sounds like a b-list rap group ). I've also puzzled over the physical meaning of these terms. It's rather like trying to imagine higher dimensional shapes. One dimension up is about all I can muster, which in this case is Jerk. Standing on a carousel, with the speed increasing and decreasing sinusoidally, ought to do it. Perhaps a better term would be "projectile vomiting" rather than jerk, huh??? (grin). ================================================== Now Kessler realises that you have got to put yourself in the car. But Horselover has gone one better hasn't he. He has put himself on a carousel. If he nails a car seat to the floor he can experience acceleration on a continuous basis whereas in a car travelling in a straight line Kessler can only experience it on a sinusoidal basis - or to be more general a cyclical basis. But if the carousel governor gets castrated (the mechanism, not the owner) and the music goes faster and faster, though Horselover will experience increasing acceleration, he will also get very giddy and might even start, in his own words, "projectile vomiting". This is because the increasing acceleration sensed by the nerves in his back is monotonically coupled to the increasing rotation sensed by his semi circular canals (SCC). Kessler doesn't have this problem. How can we uncouple these two sensation to prevent Horselover from getting sick. Well one solution I rather fancy would be to operate on Fats and cut out his SCCs ;-) . that together with panel nailed round the outside of the carousel should do the trick. But I'm sure Horselover would prefer the solution familiar to all science fiction fans, namely, we just make the Carousel big enough to reduce the rotational speed below the threshold of perception. So we have now produced the "pure" sensation of continuous acceleration by reducing the rotation until we can't sense it. What about the next step? What about rate of change of acceleration? What about jerk? Well, if Kessler is accelerating over speed bumps he will experience plenty of cyclical jerk along with his cyclical acceleration. And even though we may have given Fats continuous acceleration without perceptible rotation by making the carousel big enough, he will still experience cyclical jerk from the floor of the carousel going up and down as carousels often do. Now in order not to confuse the reader more than necessary I will substitute a large 1st order gyro for the carousel and four second order gyros to simulate the up and down motion of the gyro floor. Because by now Horselover Fats has suffered enough we will substitute the saloon chanteuse Frenchy (Marlene Dietrich) who has taken umbrage at Horselover's indifferent reaction to her charms and vows to make a fool of him. The position of Frenchy on the second order gyro is shown by the flag in http://www.grimer2.freeserve.co.uk/pge25.htm Next we can give Marlene the *Jerry Bounce* (jounce) sensation by substituting the 2nd order gyros by pairs of 3rd gyros {I would have continued with quad gyros but the drawing was getting more crowded than Diana's marriage ;-) ] http://www.grimer2.freeserve.co.uk/pge26.htm This process can be continued indefinitely and Dietrich can be subjected in principle to whatever order of motion we care to imagine. But consider this. We are already subject to higher order derivative motions for, We are orbiting the earth Which is orbiting the sun Which is orbiting the galaxy Which is orbiting ......... And I've probably left out quite a few stages. So we are actually experiencing d[^n]L / dt[^n] motion. Fortunately we don't have any sense mechanisms to detect d[^(n-1)]L / dt[^(n-1)] and lower order motions or we would be very sick indeed with mal de terre, etc. Clearly, down to the scale of man, there is a relationship between scale and derivative motion. The smaller the object the higher the derivative motion. It is not unreasonable to infer that on the scale of molecules and atoms and nuclei and .... the objects are subject to even higher derivative motions than we are. We can produce a few orders of these motions artificially with mechanical devices of the type illustrated providing the strength of our material allows. It would seem that these higher derivatives already exist naturally. Also, our senses are very limited in the motions we can detect but materials have senses we do not possess. We cannot detect the earths orbital motion but Foucault's Pendulum can. We cannot detect radio waves, etc., etc. Once one gets away from the tyranny of Cartesian geometry - the inanity of imagining that space only has three dimensions, and the utter stupidity of thinking that time only has a single dimension, then one can start thinking about the higher order derivatives of motion and how to put them to use. One might even be able to use such insights for beating the Stock Market - Now there's a thought. <grin> To lock oneself into 4 dimensions is like sticking to the shape of the 60's TV screen ( [x^4 + y^4] = 1 with suitable scaling of x and y). To get with it one needs to think in terms of much higher powers like [x^64 + y^64] = 1. for example, which will give us a nice second millennium rectangular screen. Cheers Frank Grimer ===================================== Big whorls have little whorls That feed on their velocity, And little whorls have lesser whorls And so on to viscosity. - Lewis F. Richardson - =====================================
