[continued from previous message]   
      
   >>>>>>>>>>>>>>>> while   
   >>>>>>>>>>>>>>>> others are dots to connect in what must otherwise be   
   >>>>>>>>>>>>>>>> not-particles.   
   >>>>>>>>>>>>>>>> (... Which are valleys or ridges among waves and it's   
   >>>>>>>>>>>>>>>> falsifiable   
   >>>>>>>>>>>>>>>> and demonstrable effects about and around them, or,   
   >>>>>>>>>>>>>>>> Feynman on   
   >>>>>>>>>>>>>>>> the Stern-Gerlach apparatus demands a continuum mechanics.)   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> About continuity and line-drawing [0, 1], of course it's   
   >>>>>>>>>>>>>>>> one   
   >>>>>>>>>>>>>>>> of the very oldest of notions and one of Aristotle's   
   >>>>>>>>>>>>>>>> continua,   
   >>>>>>>>>>>>>>>> that there are at least three models of mathematical   
   >>>>>>>>>>>>>>>> continuous   
   >>>>>>>>>>>>>>>> domains, that, each with with their own regularity and   
   >>>>>>>>>>>>>>>> ruliality   
   >>>>>>>>>>>>>>>> of completeness, yet each to each other beyond an inductive   
   >>>>>>>>>>>>>>>> impasse,   
   >>>>>>>>>>>>>>>> have for wider reason and itself rationality, that the   
   >>>>>>>>>>>>>>>> repleteness   
   >>>>>>>>>>>>>>>> of their completeness, has a pre-Cartesian   
   >>>>>>>>>>>>>>>> "only-diagonal" and   
   >>>>>>>>>>>>>>>> then for that the rationals are HUGE, keeping it then   
   >>>>>>>>>>>>>>>> altogether   
   >>>>>>>>>>>>>>>> that in extra-ordinary foundations of mathematics, a MODERN   
   >>>>>>>>>>>>>>>> mathematics,   
   >>>>>>>>>>>>>>>> that it rescues modern mathematics from blindness (in its   
   >>>>>>>>>>>>>>>> dumbness).   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> If you didn't play Zork in the 80's then I suppose you   
   >>>>>>>>>>>>>>>> weren't around or didn't have a computer or didn't have   
   >>>>>>>>>>>>>>>> a copy of Zork. It's a text-based adventure.   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> So, I suppose there may be other reasons, though here   
   >>>>>>>>>>>>>>>> there's   
   >>>>>>>>>>>>>>>> that all the reasons and none sort of result at least one.   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> Yeah, I imagine if you let Kosmanson go on then there'd   
   >>>>>>>>>>>>>>>> be quite more to it.   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> A note about Kosmanson's emphasis on what's often   
   >>>>>>>>>>>>>>> truncated in an   
   >>>>>>>>>>>>>>> infinite series. A year or so back I was forming baby   
   >>>>>>>>>>>>>>> problems in a   
   >>>>>>>>>>>>>>> blog   
   >>>>>>>>>>>>>>> for a Linux newsgroup frequenters to solve, and in one of   
   >>>>>>>>>>>>>>> them one   
   >>>>>>>>>>>>>>> would   
   >>>>>>>>>>>>>>> begin with a correct equation, would make correct changes   
   >>>>>>>>>>>>>>> in it,   
   >>>>>>>>>>>>>>> but   
   >>>>>>>>>>>>>>> would end up in an obviously wrong equation :) Nobody   
   >>>>>>>>>>>>>>> solved it of   
   >>>>>>>>>>>>>>> course (audience were mostly morons). But I now wonder if   
   >>>>>>>>>>>>>>> that   
   >>>>>>>>>>>>>>> problem   
   >>>>>>>>>>>>>>> had something about Kosmanson's concerns about handling   
   >>>>>>>>>>>>>>> infinities.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> Here I quote the part of the blog that contained that   
   >>>>>>>>>>>>>>> problem:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> (beginning of the quote)   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>    "Then, swoooooooshhshsh!.... and Jesus and all that   
   >>>>>>>>>>>>>>> intense   
   >>>>>>>>>>>>>>> light   
   >>>>>>>>>>>>>>> went   
   >>>>>>>>>>>>>>> back up and out of there. Physfit looked up and there wasn't   
   >>>>>>>>>>>>>>> even an   
   >>>>>>>>>>>>>>> opening in the ceiling anymore. But now for some reason   
   >>>>>>>>>>>>>>> he was   
   >>>>>>>>>>>>>>> horizontally on the floor, in his bed. Right in the   
   >>>>>>>>>>>>>>> living room!   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> He thought a bit about what was happening, when he found   
   >>>>>>>>>>>>>>> himself   
   >>>>>>>>>>>>>>> quite   
   >>>>>>>>>>>>>>> hungry. Last time he had eaten anything was the night   
   >>>>>>>>>>>>>>> before he had   
   >>>>>>>>>>>>>>> waken up on the summit of the magic mountain in an urban   
   >>>>>>>>>>>>>>> Dallas   
   >>>>>>>>>>>>>>> area.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> He thought to himself, "I'm going to assume that more   
   >>>>>>>>>>>>>>> than 48   
   >>>>>>>>>>>>>>> hours has   
   >>>>>>>>>>>>>>> passed since. So got up and walked to the kitchen and   
   >>>>>>>>>>>>>>> took a look   
   >>>>>>>>>>>>>>> inside   
   >>>>>>>>>>>>>>> refrigerator. There was nothing there but the cat food he   
   >>>>>>>>>>>>>>> had   
   >>>>>>>>>>>>>>> cooked on   
   >>>>>>>>>>>>>>> the day he first saw the magic mountain. He got on the   
   >>>>>>>>>>>>>>> computer to   
   >>>>>>>>>>>>>>> order   
   >>>>>>>>>>>>>>> something zesty from HelloFresh. After choosing the   
   >>>>>>>>>>>>>>> closest to a   
   >>>>>>>>>>>>>>> healthy   
   >>>>>>>>>>>>>>> nice pre-agricultural food kit, he clicked, "Go to checkout"   
   >>>>>>>>>>>>>>> button,   
   >>>>>>>>>>>>>>> after which the computer waited for a few seconds but   
   >>>>>>>>>>>>>>> instead of   
   >>>>>>>>>>>>>>> getting   
   >>>>>>>>>>>>>>> to the check out screen, a screen came up to make sure   
   >>>>>>>>>>>>>>> Physfit was   
   >>>>>>>>>>>>>>> not a   
   >>>>>>>>>>>>>>> robot. It had a simple question that he had to give it   
   >>>>>>>>>>>>>>> the correct   
   >>>>>>>>>>>>>>> answer, otherwise food nommo.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> The question went like this:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>      "In math, is there a difference between the two numbers   
   >>>>>>>>>>>>>>> 0.999999...   
   >>>>>>>>>>>>>>> and 1 ?"   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> The digits of "9" continued forever to the right of the   
   >>>>>>>>>>>>>>> radix   
   >>>>>>>>>>>>>>> point. So   
   >>>>>>>>>>>>>>> of course, Physfit clicked on the "yes" button. If there   
   >>>>>>>>>>>>>>> was not a   
   >>>>>>>>>>>>>>> difference, then one wouldn't even bother to write 1 in   
   >>>>>>>>>>>>>>> that funky   
   >>>>>>>>>>>>>>> form,   
   >>>>>>>>>>>>>>> using an infinite series of digit 9.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> But the screen disappeared, and a message said, "You're a   
   >>>>>>>>>>>>>>> robot.   
   >>>>>>>>>>>>>>> Bye!"   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> Physfit said, "Fuck!" (first of the fix number of curses   
   >>>>>>>>>>>>>>> Jesus had   
   >>>>>>>>>>>>>>> allowed him for that day). So he took a pen and paper and   
   >>>>>>>>>>>>>>> started   
   >>>>>>>>>>>>>>> jotting down:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>      x = 0.99999....   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> Therefore:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>      10x = 9.99999....   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> Now he subtracted the former from the latter:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>      10x - x = 9.99999... - 0.99999...   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> Which simplifies to:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>      9x = 9   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> And therefore:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>      x = 1   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> "What the fuck??", said Physfit (his 2nd curse of the day).   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> Why x which was 0.99999... and not 1, turned out to be 1?   
   >>>>>>>>>>>>>>> ... "   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> (end of quote)   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> So, is this problem pointing to what Kosmanson has been   
   >>>>>>>>>>>>>>> so keen   
   >>>>>>>>>>>>>>> about? :)   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> Once I was reading a book or article,   
   >>>>>>>>>>>>>> and was introduced the introduction of .999 (...),   
   >>>>>>>>>>>>>> vis-a-vis, 1. A cohort of subjects was surveyed   
   >>>>>>>>>>>>>> their opinion and belief whether .999, dot dot dot,   
   >>>>>>>>>>>>>> was equal to, or less than, one. About half said   
   >>>>>>>>>>>>>> same and about half said different.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
      
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