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#41
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On Jul 8, 2:46*pm, riverman wrote:
In a similar vein, the old Rand McNally Road Atlas used to have (maybe still does...) a great page in the back where it showed a few hundred cities as dots, and had little red lines connecting them, approximating the road networks. The lines were labeled with the distance and time required to travel between these adjacent cities. In my younger days I used to drive all over the place...a very similar pattern to my older life it appears....and relied on this page a lot for determining my route. I discovered that it was impossible to determine the best route from LA to Boston, as there were only short segments, but I assumed that if point C lay somewhere between point A and point B, then the shortest distance from A to C, then C to B, would be the shortest distance from A to C. Then, of course, add point D between A and C, and point E between A and D, etc.....and strangely enough...I soon found that the shortest distance from A to C worked itself out from the details. Very similar to the approach taken by Messrs. Lewis, Clark, Thompson, Humboldt (not necessarily in chronological order) etc. Of course, these and their ilk generally left more, and more explicit and accurate, directions than they found.....but they and their immediate successors would have found the whole process eerily familiar and instantly recognizable and useful. Seems obvious Yes, it does. (and was later proven with mathematical studies of Hamiltonian Paths and Euler Circuits and Dijkstra's Algorithm) Wouldn't know.....never heard of any of those. but you'd be suprised how many people will take the long (time and distance) route around town on a highway rather than the short (time and distance) route through town just because they are in love with feeling motion. Maybe. Probably not. Not easily surprised in these latter days. Travelling 60mph for a half hour seems like its 'faster' than travelling 30 mph for 25 minutes, yet people do it. Travelling 60 mph for whatever length of time is "faster" than travelling 30 mph for whatever length of time......twice as fast, as a matter of fact. Travelling 60 mph will also get you to wherever you are going in exactly half the time as moving toward it at thirty miles per hour over the same route. On the other hand, if we're dealing with different routes then making the trip in 25 minutes at 30 mph would appear (at first glance) to offer obvious and insurmountable advantages to travelling at 60 mph hour for 30 minutes to the same destination. That's the trouble with first glances. In fact, I deal with an uncannily similar situation daily (more or less) on my way to work in the mornings. I can take a 6 mile route over "surface streets" or a bit more than twice as long route via the freeway. The freeway route takes an average of about a minute longer despite the much higher (more than double) average speed.....most days. Just about a horse apiece.....slight advantage to the surface streets. But..... But the surface streets are littered with 17 traffic lights. If I hit them all wrong the balance tilts WAY over to the freeway side in terms of travel time. And, in any case, the fuel savings via the freeway (no stop and start) tilt heavily in it's favor regardless of a few seconds difference in travel time. I think most people don't really think, let alone analyze, when they are doing stuff. Maybe. But it could just be more a question of what they think about and what analytical tools and data they have at their disposal, the former being highly dependent on the latter. Its refreshing to hear stories of people who do. Yeah......generally. But then we run into people who do it badly.....and that's at least as distressing as people who don't do it at all, ainna? I mean, look at the diminutive member, the kennies, davie, etc. You'd truly enjoy the opening chapter of "Beyond Numeracy' by John Allen Paulos. You're assuming I'd understand it. That's flattering.....or naive. ![]() giles |
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On Jul 8, 10:20*pm, MajorOz wrote:
On Jul 8, 2:46*pm, riverman wrote: On Jul 8, 6:17*pm, Giles wrote: The question that arises is whether or not it's worth the bother to pursue the closest approximation to a straight line that is possible on a given route. *That is to say, over the course of, say, a thousand mile cross-country trip, is there a substantial savings in mileage and time to be gained by taking the inside lane in each curve, switching lanes as necessary and taking the shortest, straightest path possible between successive curves? Don't know. * In a similar vein, the old Rand McNally Road Atlas used to have (maybe still does...) a great page in the back where it showed a few hundred cities as dots, and had little red lines connecting them, approximating the road networks. The lines were labeled with the distance and time required to travel between these adjacent cities. In my younger days I used to drive all over the place...a very similar pattern to my older life it appears....and relied on this page a lot for determining my route. I discovered that it was impossible to determine the best route from LA to Boston, as there were only short segments, but I assumed that if point C lay somewhere between point A and point B, then the shortest distance from A to C, then C to B, would be the shortest distance from A to C. Then, of course, add point D between A and C, and point E between A and D, etc.....and strangely enough...I soon found that the shortest distance from A to C worked itself out from the details. Seems obvious (and was later proven with mathematical studies of Hamiltonian Paths and Euler Circuits and Dijkstra's Algorithm) but you'd be suprised how many people will take the long (time and distance) route around town on a highway rather than the short (time and distance) route through town just because they are in love with feeling motion. Travelling 60mph for a half hour seems like its 'faster' than travelling 30 mph for 25 minutes, yet people do it. I think most people don't really think, let alone analyze, when they are doing stuff. Its refreshing to hear stories of people who do. You'd truly enjoy the opening chapter of "Beyond Numeracy' by John Allen Paulos. --riverman I have always considered the best route to be neither the shortest nor the quickest, but that which resulted in the least hassle. * That is the reason I won't, for instance, go straight through a large city, with its stoplights, emergency vehicles, etc, and prefer, usually, the beltways. I-894.....this afternoon.....en route from Wauwatosa to Burlington.....by far the shortest, fastest and least frustrating route. Semi on fire.....3 lanes at a standstill.....who knew? However, for the same reason, I don't cross Wyoming on I-80, unless I am in a hurry. *I prefer US 30. *It is more peaceful, scenery is better, and there are fewer 18-wheelers (except in snow, when I-80 is closed and ALL THE TRUCKS clog up US 30) I don't cross Wyoming at all. Much peace of mind. Enjoy the blue highways Or take a nice peaceful boat ride all the way up the Missouri.....more or less.....sorta. (Wm. Leastheat Moon) oz- hippopotamus amphibius been there.....read that. |
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On Jul 9, 6:02*am, Giles wrote:
On Jul 8, 2:46*pm, riverman wrote: You'd truly enjoy the opening chapter of "Beyond Numeracy' by John Allen Paulos. You're assuming I'd understand it. *That's flattering.....or naive. * * * * * ![]() I'm very certain that you'd understand it, and only slightly less certain that you would enjoy it. He recounts his musings while driving (along the NJ Tpk, I believe). It's a fascinating and entertaining insight into how the mind wanders with a completely understandable mathematical/logical bent. If you enjoy compendi of mathematical oddities, puzzles, trivia, etc. then this is a satisfying read, The rest of the book may or may not be to your liking, but the prequel; "Innumeracy" is definitely readable by the layman and has gotten rave reviews and awards from all sorts of quarters. --riverman |
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On Jul 9, 1:00*pm, riverman wrote:
On Jul 9, 6:02*am, Giles wrote: On Jul 8, 2:46*pm, riverman wrote: You'd truly enjoy the opening chapter of "Beyond Numeracy' by John Allen Paulos. You're assuming I'd understand it. *That's flattering.....or naive. * * * * * ![]() I'm very certain that you'd understand it, and only slightly less certain that you would enjoy it. He recounts his musings while driving (along the NJ Tpk, I believe). It's a fascinating and entertaining insight into how the mind wanders with a completely understandable mathematical/logical bent. If you enjoy compendi of mathematical oddities, puzzles, trivia, etc. then this is a satisfying read, The rest of the book may or may not be to your liking, but the prequel; "Innumeracy" is definitely readable by the layman and has gotten rave reviews and awards from all sorts of quarters. --riverman "Innumeracy" rings a bell. I may have a copy lying around somewhere.....though I haven't read it. Anyway, I looked it up and found this: http://www.innumeracy.com/ Hofstadter's "Metamagical Themas" rings a very loud bell. One of my favorite books. Opened up a whole new world to me. I've read it three or four times......just about time for another reading*. Meanwhile, I don't particularly enjoy mathematical works in general.....not even those that cater especially to the mathematically handicapped like myself. I periodically subject myself to such material out of an occasional vain hope that exposure (however remedial) will some day result in enlightenment.....or at least a sustained interest. It never works. giles *others of hofstadter's works i've delved into, particularly "Gödel, Escher, Bach: an Eternal Golden Braid", and "Le Ton beau de Marot: In Praise of the Music of Language," are so opaque to me that they might as well have been written in some encrypted obscure martian dialect. |
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On Jul 11, 4:06*am, Giles wrote:
On Jul 9, 1:00*pm, riverman wrote: On Jul 9, 6:02*am, Giles wrote: On Jul 8, 2:46*pm, riverman wrote: You'd truly enjoy the opening chapter of "Beyond Numeracy' by John Allen Paulos. You're assuming I'd understand it. *That's flattering.....or naive. * * * * * ![]() I'm very certain that you'd understand it, and only slightly less certain that you would enjoy it. He recounts his musings while driving (along the NJ Tpk, I believe). It's a fascinating and entertaining insight into how the mind wanders with a completely understandable mathematical/logical bent. If you enjoy compendi of mathematical oddities, puzzles, trivia, etc. then this is a satisfying read, The rest of the book may or may not be to your liking, but the prequel; "Innumeracy" is definitely readable by the layman and has gotten rave reviews and awards from all sorts of quarters. --riverman "Innumeracy" rings a bell. *I may have a copy lying around somewhere.....though I haven't read it. *Anyway, I looked it up and found this: http://www.innumeracy.com/ Hofstadter's "Metamagical Themas" rings a very loud bell. *One of my favorite books. *Opened up a whole new world to me. *I've read it three or four times......just about time for another reading*. Meanwhile, I don't particularly enjoy mathematical works in general.....not even those that cater especially to the mathematically handicapped like myself. *I periodically subject myself to such material out of an occasional vain hope that exposure (however remedial) will some day result in enlightenment.....or at least a sustained interest. *It never works. giles *others of hofstadter's works i've delved into, particularly "Gödel, Escher, Bach: an Eternal Golden Braid", and "Le Ton beau de Marot: In Praise of the Music of Language," are so opaque to me that they might as well have been written in some encrypted obscure martian dialect. Goedel, Escher, Bach generated such a cult following that I was unable to give it a real fair trial. But I find that 'Pop Math' books bore me, while rigorous mathematical texts blow me out of the water. I have a very narrow range of readable mathematical books...almost entirely limited to historical biographies that give a context to major discoveries. Let me know if you get into Innumeracy....and the opening chapter of Beyond Numeracy. I'll take a gander at Metamagica Themas. --riverman |
#46
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![]() "riverman" wrote in message ... On Jul 5, 12:01 pm, rw wrote: the rod later, it was jammed. Although I was able to get the sections apart using the 'behind the knee' method, I--riverman Hi Myron, A straight in-line pull is needed and the behind the knee method is one. I was taught a slightly different approach - if you have a friend handy - let's call the friend A and me B With the ferrule between A and B, A takes a firm grip with one hand on B's side of the ferrule and close to it, and the other hand about 18" on the other (his) side of the ferrule. B then takes a firm grip with one hand on A's side of the ferrule and close to it then, the other hand about 18" from the ferrule on his side. Now pull steadily and the joint will come apart. This is much easier to demonstrate that to explain - usually the case with simple manoeuvres Bill |
#47
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On Jul 11, 11:57*am, riverman wrote:
Goedel, Escher, Bach generated such a cult following that I was unable to give it a real fair trial. I wasn't aware of that cult following until I read a bit more about Hofstadter last night. I guess nobody I know reads that kind of stuff.....or none admit to it anyway. I gave it my best up to about the middle of the book and then gave up in utter stupified bewilderment. The same for "Le Ton beau de Marot" though giving up on this one was easier to justify with a more or less intact ego because much of it actually WAS in another language.....several others, to be more precise. But I find that 'Pop Math' books bore me, Ditto.....with a few notable exceptions. while rigorous mathematical texts blow me out of the water. Ditto.....in spades. I have a very narrow range of readable mathematical books...almost entirely limited to historical biographies that give a context to major discoveries. Even that doesn't spark any interest here. But speaking of biography, see below.* Let me know if you get into Innumeracy....and the opening chapter of Beyond Numeracy. Will do. But don't hold your breath. My reading these days is dictated primarily by kicking the piles and seeing what falls out.....it could be a while. ![]() I'll take a gander at Metamagica Themas. Hope you enjoy it. giles * http://alturl.com/fug9t HUZZAH! |
#48
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On Jul 11, 8:12*pm, Giles wrote:
On Jul 11, 11:57*am, riverman wrote: Goedel, Escher, Bach generated such a cult following that I was unable to give it a real fair trial. I wasn't aware of that cult following until I read a bit more about Hofstadter last night. *I guess nobody I know reads that kind of stuff.....or none admit to it anyway. *I gave it my best up to about the middle of the book and then gave up in utter stupified bewilderment. *The same for "Le Ton beau de Marot" though giving up on this one was easier to justify with a more or less intact ego because much of it actually WAS in another language.....several others, to be more precise. But I find that 'Pop Math' books bore me, Ditto.....with a few notable exceptions. while rigorous mathematical texts blow me out of the water. Ditto.....in spades. I have a very narrow range of readable mathematical books...almost entirely limited to historical biographies that give a context to major discoveries. Even that doesn't spark any interest here. *But speaking of biography, see below.* Let me know if you get into Innumeracy....and the opening chapter of Beyond Numeracy. Will do. *But don't hold your breath. *My reading these days is dictated primarily by kicking the piles and seeing what falls out.....it could be a while. * * * ![]() I'll take a gander at Metamagica Themas. Hope you enjoy it. giles * *http://alturl.com/fug9t HUZZAH! Perhaps "the" pop science" book is _One, Two, Three...Infinity_, by George Gamow. Also pretty good are almost any 'splain books by Isaac Asimov. cheers oz |
#49
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On Jul 11, 11:10*pm, MajorOz wrote:
Perhaps "the" pop science" book is _One, Two, Three...Infinity_, by George Gamow. I'm pretty sure I've read something or other by Gamow at one time or another.....but not at all sure what it was. Anyway, looking him up led to Hoyle, Hubble, Crick, the Kalam cosmological argument, Hume, empiricism, Boswell, Johnson, dictionaries....... An altogether delightful evening's romp through the Elysian/illusion/ allusion/elision(no mention of the Aleutians thus far) fields. Thanks. Also pretty good are almost any 'splain books by Isaac Asimov. Certainly among the most readable of polymaths. cheers oz prosit. giles |
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