Author: Robert Hyatt
Date: 09:14:18 10/02/01
Go up one level in this thread
On October 02, 2001 at 11:06:34, Miguel A. Ballicora wrote: >On October 02, 2001 at 10:38:02, Robert Hyatt wrote: > >>On October 02, 2001 at 04:54:13, Bruce Moreland wrote: >> >>>On October 01, 2001 at 00:36:48, Robert Hyatt wrote: >>> >>>>On September 30, 2001 at 14:47:21, Bruce Moreland wrote: >>>> >>>>>On September 29, 2001 at 14:54:03, Robert Hyatt wrote: >>>>> >>>>>>On September 29, 2001 at 10:41:37, Miguel A. Ballicora wrote: >>>>> >>>>>>>Super-linear speedups are "probably" impossible but so far I did not see that >>>>>>>they are "provably" impossible. I would settle with "They are believed to be >>>>>>>impossible". >>>>>>> >>>>>>>Regards, >>>>>>>Miguel >>>>>> >>>>>> >>>>>>They simply _are_ impossible. Unless you believe in perpetual >>>>>>motion, infinite compression, a fire that will burn forever, etc. >>>>> >>>>>Take a human who can move a 200-pound box, but only by scraping it along the >>>>>ground. Compute the time it takes him to move 10 such boxes 100 yards. >>>>> >>>>>Assume that two humans can move a 200-pound box more easily. Can they move a >>>>>200-pound box more than twice as fast as one human? Would this violate laws >>>>>against perpetual motion? Of course not. It is perfectly valid to consider >>>>>working in parallel rather than working serially. The mechanics of the task >>>>>might change, resulting in much increased efficiency -- they can lift the box >>>>>off the ground. >>>> >>>> >>>>I think that after you think about this example, you will see the flaw. >>>>Lifting the box off the ground takes _more_ effort. So the two people are >>>>doing _more_ work in a given period of time than two people pushing two boxes >>>>at the same time. The ancient Egyptions found that dragging was better than >>>>lifting. :) >>>> >>>> >>>> >>>>> >>>>>Two workers cooperating to perform a task, do not *have* to go less than or >>>>>equal to the speed of two workers, each of whom does exactly half of a task that >>>>>can be fairly divided in two. >>>>> >>>>>There exists the opportunity for synergy. >>>>> >>>>>The argument that the above violates the prohibition against perpetual motion is >>>>>fallacious. >>>>> >>>>>bruce >>>> >>>> >>>>Not after you think about it. If two people work and each of them moves 5 >>>>blocks, then they do no more work than the 1 person did moving 10. But they >>>>did it in twice the time. If they _lift_ the block _and_ move it, they are >>>>doing _more_ work per unit of time. They should have moved the blocks >>>>faster one at a time, but they were taking it easy... >>>> >>>> A computer can't do that. >>> >>>You can't possibly be arguing that there is nothing that N (N>1) people can't do >>>in less than 1/N the time that it takes one person. >>> >>>I was trying to find an obvious example. If you don't like that one, I'm sure >>>there is another one. >>> >>>bruce >> >> >>If you mean something that takes one person N units of time to do, and two >>can do it in less than N/2 units of time, then no, I don't believe it is >>possible. The exception is that I have to move a 400 pound box. I can't >>move it by myself, probably. So I can't do it at all. Two people can >>probably shove it around. > >Bruce's example was just perfect. Many objects can be lifted and moved fast >but they can hardly be pushed. The important factor is both the friction (static >and dynamic) of the floor, if it is too big you better lift it. Do the physics first. It take energy to lift the object. And it takes energy to move it. If you lift and walk, while I drag, then most likely I will do less work. Only if the friction is so prohibitive as to overcome the cost of lifting, will that be more economical. Otherwise everyone would be flying rather than using trains, automobiles, busses, and their feet. >That is simple mechanics. (another factor is the friction of your shoes should >not be low to push, otherwise you slip) >For instance, the table I have in the grass at home is a good example. >I better have help to lift it and move it, because pushing will take me forever. >(or never, if the static friction is too big so I cannot even start moving >the object, it is like a threshold). Time isn't the issue. In a chess tree, there is no slippage. No friction. No hills. No valleys. No nothing. Just a precise amount of work that must be done to dismiss each and every node in the tree. The amount of work for each node is exactly the same, whether it is done by 1 processor or by 100. In the case of moving the object, just compute the total work done to lift and move it, vs dragging it. If your feet slip when dragging, they will also slip after lifting when you try to accelerate or stop the object as you move it. Same laws apply to either case... Coefficient of friction is too low, it isn't going anywhere whether you lift it or drag it. You can't apply power to it no matter what. But we can take a 200lb block of concrete, and move it down a 100 meter hallway, and calculate the work done by carrying it and by sliding it. Carrying it is much harder. > >As I said, I hate to be discussing analogies because we end up discussing >things that are not relevant, but I could not resist since Bruce's example >is just perfect. Perfect for what? Not to compare against a parallel tree search. And not to use when discussing something like conservation of energy, where you have so much energy to do a given task. Finding faster solutions always involves expending _more_ energy. IE think E = MV^2... > >Regards, >Miguel > > >> >>But I can't think of any thing that one can do, where two can do it twice as >>fast, assuming that two don't do more physical work than the one person did. >>Otherwise it isn't reasonable, as it would be like comparing two 1ghz processors >>to one 800mhz processor. The two 1 gigs should run more than twice as fast. >>They are doing more than twice as much work. >> >>If you can find an example, it would be interesting to analyze it. Either both >>do more work than one would do, or else there is a trick involved. IE you have >>to simultaneously nail up both ends of a long board. One person has to walk >>back and forth multiple times. Two would not. But in that case, the two-person >>team eliminated work required of the one person team, _before_ the project even >>starts. I don't see any possible analogy applied to alpha/beta search.
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