[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.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>

[continued in next message]

--- SoupGate-DOS v1.05
 * Origin: you cannot sedate... all the things you hate (1:229/2)